[{"scopus_import":"1","ec_funded":1,"citation":{"ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. 2023;33(4):2981-3009. doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","apa":"Ding, X., &#38; Ji, H. C. (2023). Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>","ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009.","mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>."},"acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","date_published":"2023-08-01T00:00:00Z","external_id":{"isi":["001031710500012"],"arxiv":["2010.16083"]},"corr_author":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1214/22-aap1882","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"day":"01","article_type":"original","issue":"4","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2010.16083","open_access":"1"}],"status":"public","month":"08","isi":1,"author":[{"full_name":"Ding, Xiucai","first_name":"Xiucai","last_name":"Ding"},{"last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"quality_controlled":"1","publication":"The Annals of Applied Probability","intvolume":"        33","date_updated":"2025-09-09T14:12:00Z","volume":33,"page":"2981-3009","abstract":[{"lang":"eng","text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. "}],"arxiv":1,"year":"2023","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"language":[{"iso":"eng"}],"publisher":"Institute of Mathematical Statistics","type":"journal_article","oa":1,"article_processing_charge":"No","publication_status":"published","oa_version":"Preprint","fulldoi":"https://doi.org/10.1214/22-aap1882","date_created":"2024-01-08T13:03:18Z","publication_identifier":{"issn":["1050-5164"]},"title":"Local laws for multiplication of random matrices","_id":"14750","department":[{"_id":"LaEr"}]},{"article_processing_charge":"No","oa":1,"oa_version":"Preprint","fulldoi":"https://doi.org/10.1214/22-aap1826","publication_status":"published","publication_identifier":{"issn":["1050-5164"]},"date_created":"2024-01-10T09:23:31Z","department":[{"_id":"LaEr"}],"title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","_id":"14775","date_updated":"2025-04-14T07:57:19Z","intvolume":"        33","arxiv":1,"abstract":[{"text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble.","lang":"eng"}],"volume":33,"page":"677-725","publisher":"Institute of Mathematical Statistics","type":"journal_article","year":"2023","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"doi":"10.1214/22-aap1826","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","article_type":"original","month":"02","status":"public","isi":1,"author":[{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli"},{"last_name":"Xu","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"issue":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2108.02728","open_access":"1"}],"publication":"The Annals of Applied Probability","quality_controlled":"1","ec_funded":1,"scopus_import":"1","citation":{"mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>.","ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","apa":"Schnelli, K., &#38; Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. 2023;33(1):677-725. doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>"},"date_published":"2023-02-01T00:00:00Z","acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]}},{"article_processing_charge":"No","oa":1,"fulldoi":"https://doi.org/10.1214/23-aop1643","oa_version":"Preprint","publication_status":"published","publication_identifier":{"issn":["0091-1798"]},"date_created":"2024-01-22T08:08:41Z","department":[{"_id":"LaEr"}],"_id":"14849","title":"On the rightmost eigenvalue of non-Hermitian random matrices","intvolume":"        51","date_updated":"2025-09-09T14:23:34Z","abstract":[{"text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.","lang":"eng"}],"arxiv":1,"page":"2192-2242","volume":51,"type":"journal_article","publisher":"Institute of Mathematical Statistics","language":[{"iso":"eng"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"year":"2023","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1214/23-aop1643","article_type":"original","day":"01","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan"}],"status":"public","isi":1,"month":"11","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"issue":"6","publication":"The Annals of Probability","quality_controlled":"1","ec_funded":1,"scopus_import":"1","citation":{"mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>"},"date_published":"2023-11-01T00:00:00Z","acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","corr_author":"1","external_id":{"isi":["001112165000004"],"arxiv":["2206.04448"]}},{"article_processing_charge":"No","oa":1,"fulldoi":"https://doi.org/10.1214/22-ejp838","oa_version":"Published Version","publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"date_created":"2023-01-16T10:04:38Z","department":[{"_id":"LaEr"}],"_id":"12290","title":"Optimal multi-resolvent local laws for Wigner matrices","intvolume":"        27","date_updated":"2025-04-14T07:57:19Z","file":[{"creator":"dernst","file_id":"12464","content_type":"application/pdf","checksum":"bb647b48fbdb59361210e425c220cdcb","relation":"main_file","date_updated":"2023-01-30T11:59:21Z","file_name":"2022_ElecJournProbability_Cipolloni.pdf","access_level":"open_access","success":1,"file_size":502149,"date_created":"2023-01-30T11:59:21Z"}],"abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"page":"1-38","volume":27,"type":"journal_article","publisher":"Institute of Mathematical Statistics","language":[{"iso":"eng"}],"year":"2022","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1214/22-ejp838","article_type":"original","license":"https://creativecommons.org/licenses/by/4.0/","day":"12","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"status":"public","isi":1,"ddc":["510"],"month":"09","publication":"Electronic Journal of Probability","quality_controlled":"1","ec_funded":1,"scopus_import":"1","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>"},"date_published":"2022-09-12T00:00:00Z","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file_date_updated":"2023-01-30T11:59:21Z","acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","has_accepted_license":"1","corr_author":"1","external_id":{"isi":["000910863700003"]}},{"day":"24","article_type":"original","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1088/1742-5468/ac9828","publication":"Journal of Statistical Mechanics: Theory and Experiment","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"10598"}]},"quality_controlled":"1","month":"11","ddc":["510","530"],"status":"public","isi":1,"author":[{"last_name":"Mondelli","first_name":"Marco","orcid":"0000-0002-3242-7020","full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"last_name":"Venkataramanan","full_name":"Venkataramanan, Ramji","first_name":"Ramji"}],"issue":"11","citation":{"ieee":"M. Mondelli and R. Venkataramanan, “Approximate message passing with spectral initialization for generalized linear models,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2022, no. 11. IOP Publishing, 2022.","ama":"Mondelli M, Venkataramanan R. Approximate message passing with spectral initialization for generalized linear models. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2022;2022(11). doi:<a href=\"https://doi.org/10.1088/1742-5468/ac9828\">10.1088/1742-5468/ac9828</a>","chicago":"Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with Spectral Initialization for Generalized Linear Models.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2022. <a href=\"https://doi.org/10.1088/1742-5468/ac9828\">https://doi.org/10.1088/1742-5468/ac9828</a>.","apa":"Mondelli, M., &#38; Venkataramanan, R. (2022). Approximate message passing with spectral initialization for generalized linear models. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/ac9828\">https://doi.org/10.1088/1742-5468/ac9828</a>","short":"M. Mondelli, R. Venkataramanan, Journal of Statistical Mechanics: Theory and Experiment 2022 (2022).","ista":"Mondelli M, Venkataramanan R. 2022. Approximate message passing with spectral initialization for generalized linear models. Journal of Statistical Mechanics: Theory and Experiment. 2022(11), 114003.","mla":"Mondelli, Marco, and Ramji Venkataramanan. “Approximate Message Passing with Spectral Initialization for Generalized Linear Models.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2022, no. 11, 114003, IOP Publishing, 2022, doi:<a href=\"https://doi.org/10.1088/1742-5468/ac9828\">10.1088/1742-5468/ac9828</a>."},"scopus_import":"1","corr_author":"1","external_id":{"isi":["000889589900001"]},"date_published":"2022-11-24T00:00:00Z","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"acknowledgement":"The authors would like to thank Andrea Montanari for helpful discussions.\r\nM Mondelli was partially supported by the 2019 Lopez-Loreta Prize. R Venkataramanan was partially supported by the Alan Turing Institute under the EPSRC Grant\r\nEP/N510129/1.","has_accepted_license":"1","file_date_updated":"2023-02-02T08:35:52Z","oa_version":"Published Version","fulldoi":"https://doi.org/10.1088/1742-5468/ac9828","publication_status":"published","article_processing_charge":"Yes (via OA deal)","oa":1,"department":[{"_id":"MaMo"}],"title":"Approximate message passing with spectral initialization for generalized linear models","_id":"12480","publication_identifier":{"issn":["1742-5468"]},"date_created":"2023-02-02T08:31:57Z","abstract":[{"lang":"eng","text":"We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the performance of AMP in the high-dimensional limit can be succinctly characterized under suitable model assumptions; AMP can also be tailored to the empirical distribution of the signal entries, and for a wide class of estimation problems, AMP is conjectured to be optimal among all polynomial-time algorithms. However, a major issue of AMP is that in many models (such as phase retrieval), it requires an initialization correlated with the ground-truth signal and independent from the measurement matrix. Assuming that such an initialization is available is typically not realistic. In this paper, we solve this problem by proposing an AMP algorithm initialized with a spectral estimator. With such an initialization, the standard AMP analysis fails since the spectral estimator depends in a complicated way on the design matrix. Our main contribution is a rigorous characterization of the performance of AMP with spectral initialization in the high-dimensional limit. The key technical idea is to define and analyze a two-phase artificial AMP algorithm that first produces the spectral estimator, and then closely approximates the iterates of the true AMP. We also provide numerical results that demonstrate the validity of the proposed approach."}],"volume":2022,"article_number":"114003","date_updated":"2025-04-15T07:50:16Z","intvolume":"      2022","file":[{"success":1,"date_created":"2023-02-02T08:35:52Z","file_size":1729997,"file_id":"12481","content_type":"application/pdf","checksum":"01411ffa76d3e380a0446baeb89b1ef7","creator":"dernst","date_updated":"2023-02-02T08:35:52Z","relation":"main_file","access_level":"open_access","file_name":"2022_JourStatisticalMechanics_Mondelli.pdf"}],"publisher":"IOP Publishing","type":"journal_article","project":[{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"year":"2022","language":[{"iso":"eng"}]},{"external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"corr_author":"1","date_published":"2022-10-01T00:00:00Z","citation":{"ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World Scientific Publishing, 2022.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036, World Scientific Publishing, 2022, doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>.","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2022. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>."},"scopus_import":"1","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"17164"}]},"quality_controlled":"1","publication":"Random Matrices: Theory and Applications","issue":"4","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"status":"public","isi":1,"month":"10","author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","first_name":"Jana","last_name":"Reker"}],"day":"01","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1142/s2010326322500368","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"year":"2022","language":[{"iso":"eng"}],"publisher":"World Scientific Publishing","type":"journal_article","volume":11,"article_number":"2250036","abstract":[{"lang":"eng","text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one."}],"arxiv":1,"intvolume":"        11","date_updated":"2026-10-02T11:31:29Z","title":"On the operator norm of a Hermitian random matrix with correlated entries","_id":"11135","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-04-08T07:11:12Z","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"publication_status":"published","oa_version":"Preprint","fulldoi":"https://doi.org/10.1142/s2010326322500368","oa":1,"article_processing_charge":"No"},{"article_type":"original","day":"01","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1214/20-aop1496","publication":"The Annals of Probability","quality_controlled":"1","author":[{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","last_name":"Dubach"},{"full_name":"Peled, Yuval","first_name":"Yuval","last_name":"Peled"}],"isi":1,"month":"07","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1904.04312","open_access":"1"}],"issue":"4","citation":{"chicago":"Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/20-aop1496\">https://doi.org/10.1214/20-aop1496</a>.","mla":"Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 49, no. 4, Institute of Mathematical Statistics, 2021, pp. 1886–916, doi:<a href=\"https://doi.org/10.1214/20-aop1496\">10.1214/20-aop1496</a>.","ista":"Dubach G, Peled Y. 2021. On words of non-Hermitian random matrices. The Annals of Probability. 49(4), 1886–1916.","apa":"Dubach, G., &#38; Peled, Y. (2021). On words of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/20-aop1496\">https://doi.org/10.1214/20-aop1496</a>","short":"G. Dubach, Y. Peled, The Annals of Probability 49 (2021) 1886–1916.","ieee":"G. Dubach and Y. Peled, “On words of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 49, no. 4. Institute of Mathematical Statistics, pp. 1886–1916, 2021.","ama":"Dubach G, Peled Y. On words of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2021;49(4):1886-1916. doi:<a href=\"https://doi.org/10.1214/20-aop1496\">10.1214/20-aop1496</a>"},"ec_funded":1,"scopus_import":"1","corr_author":"1","external_id":{"arxiv":["1904.04312"],"isi":["000681349000008"]},"date_published":"2021-07-01T00:00:00Z","acknowledgement":"The authors would like to thank Gernot Akemann, Benson Au, Paul Bourgade, Jesper Ipsen, Camille Male, Jamie Mingo, Doron Puder, Emily Redelmeier, Roland Speicher, Wojciech Tarnowski and Ofer Zeitouni for useful discussions, comments and references as well as the anonymous referee for a suggestion that greatly improved one of the theorems.\r\nG.D. gratefully acknowledges support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI), as well as the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","fulldoi":"https://doi.org/10.1214/20-aop1496","oa_version":"Preprint","publication_status":"published","article_processing_charge":"No","oa":1,"department":[{"_id":"LaEr"}],"_id":"15259","title":"On words of non-Hermitian random matrices","publication_identifier":{"issn":["0091-1798"]},"date_created":"2024-04-03T07:19:42Z","abstract":[{"lang":"eng","text":"We consider words Gi1⋯Gim involving i.i.d. complex Ginibre matrices and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word of length m is a Fuss–Catalan distribution with parameter \r\nm+1. This generalizes previous results concerning powers of a complex Ginibre matrix and products of independent Ginibre matrices. In addition, we find other combinatorial parameters of the word that determine the second-order limits of the spectral statistics. For instance, the so-called coperiod of a word characterizes the fluctuations of the eigenvalues. We extend these results to words of general non-Hermitian matrices with i.i.d. entries under moment-matching assumptions, band matrices, and sparse matrices.\r\nThese results rely on the moments method and genus expansion, relating Gaussian matrix integrals to the counting of compact orientable surfaces of a given genus. This allows us to derive a central limit theorem for the trace of any word of complex Ginibre matrices and their conjugate transposes, where all parameters are defined topologically."}],"arxiv":1,"page":"1886-1916","volume":49,"date_updated":"2025-09-10T10:13:20Z","intvolume":"        49","type":"journal_article","publisher":"Institute of Mathematical Statistics","language":[{"iso":"eng"}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"year":"2021"},{"publication_status":"published","fulldoi":"https://doi.org/10.1088/1742-5468/abc7c7","oa_version":"Published Version","oa":1,"article_processing_charge":"No","_id":"9158","title":"Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation","department":[{"_id":"MaSe"}],"date_created":"2021-02-17T17:48:46Z","publication_identifier":{"issn":["1742-5468"]},"article_number":"013101","volume":2021,"abstract":[{"text":"While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.","lang":"eng"}],"file":[{"checksum":"64e2aae4837790db26e1dd1986c69c07","content_type":"application/pdf","file_id":"9172","creator":"dernst","access_level":"open_access","file_name":"2021_JourStatMech_deNicola.pdf","relation":"main_file","date_updated":"2021-02-19T14:04:40Z","success":1,"date_created":"2021-02-19T14:04:40Z","file_size":1693609}],"date_updated":"2025-04-14T07:43:51Z","intvolume":"      2021","language":[{"iso":"eng"}],"year":"2021","project":[{"name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"type":"journal_article","publisher":"IOP Publishing","article_type":"original","day":"05","doi":"10.1088/1742-5468/abc7c7","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability","Statistical and Nonlinear Physics"],"quality_controlled":"1","publication":"Journal of Statistical Mechanics: Theory and Experiment","issue":"1","author":[{"first_name":"Stefano","orcid":"0000-0002-4842-6671","full_name":"De Nicola, Stefano","id":"42832B76-F248-11E8-B48F-1D18A9856A87","last_name":"De Nicola"}],"isi":1,"month":"01","ddc":["530"],"status":"public","citation":{"ieee":"S. De Nicola, “Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 1. IOP Publishing, 2021.","ama":"De Nicola S. Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2021;2021(1). doi:<a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">10.1088/1742-5468/abc7c7</a>","chicago":"De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2021. <a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">https://doi.org/10.1088/1742-5468/abc7c7</a>.","ista":"De Nicola S. 2021. Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation. Journal of Statistical Mechanics: Theory and Experiment. 2021(1), 013101.","apa":"De Nicola, S. (2021). Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">https://doi.org/10.1088/1742-5468/abc7c7</a>","short":"S. De Nicola, Journal of Statistical Mechanics: Theory and Experiment 2021 (2021).","mla":"De Nicola, Stefano. “Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2021, no. 1, 013101, IOP Publishing, 2021, doi:<a href=\"https://doi.org/10.1088/1742-5468/abc7c7\">10.1088/1742-5468/abc7c7</a>."},"scopus_import":"1","ec_funded":1,"external_id":{"isi":["000605080300001"]},"has_accepted_license":"1","acknowledgement":"S D N would like to thank M J Bhaseen, J Chalker, B Doyon, V Gritsev, A Lamacraft,\r\nA Michailidis and M Serbyn for helpful feedback and stimulating conversations. S D N\r\nacknowledges funding from the Institute of Science and Technology (IST) Austria, and\r\nfrom the European Union’s Horizon 2020 research and innovation program under the\r\nMarie Sk\blodowska-Curie Grant Agreement No. 754411. S D N also acknowledges funding\r\nfrom the EPSRC Center for Doctoral Training in Cross-Disciplinary Approaches to Non-\r\nEquilibrium Systems (CANES) under Grant EP/L015854/1. S D N is grateful to IST\r\nAustria for providing open access funding.","file_date_updated":"2021-02-19T14:04:40Z","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2021-01-05T00:00:00Z"},{"quality_controlled":"1","publication":"Journal of Statistical Mechanics: Theory and Experiment","issue":"6","main_file_link":[{"url":"https://arxiv.org/abs/1808.00249","open_access":"1"}],"author":[{"first_name":"Ryan J","orcid":"0000-0003-0002-1867","full_name":"Cubero, Ryan J","id":"850B2E12-9CD4-11E9-837F-E719E6697425","last_name":"Cubero"},{"last_name":"Jo","full_name":"Jo, Junghyo","first_name":"Junghyo"},{"last_name":"Marsili","first_name":"Matteo","full_name":"Marsili, Matteo"},{"last_name":"Roudi","first_name":"Yasser","full_name":"Roudi, Yasser"},{"first_name":"Juyong","full_name":"Song, Juyong","last_name":"Song"}],"month":"06","status":"public","article_type":"original","day":"17","doi":"10.1088/1742-5468/ab16c8","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["optimization under uncertainty","source coding","large deviation"],"external_id":{"arxiv":["1808.00249"]},"acknowledgement":"We acknowledge interesting discussions with M Abbott, E Aurell, J Barbier, R Monasson, T Mora, I Nemenman, N Tishby and R Zecchina. This research was supported by the Kavli Foundation and the Centre of Excellence scheme of the Research Council of Norway (Centre for Neural Computation) (RJC and YR), by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2016R1D1A1B03932264) (JJ), and, in part, by the ICTP through the OEA-AC-98 (JS).","date_published":"2019-06-17T00:00:00Z","citation":{"mla":"Cubero, Ryan J., et al. “Statistical Criticality Arises in Most Informative Representations.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6, 063402, IOP Publishing, 2019, doi:<a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">10.1088/1742-5468/ab16c8</a>.","apa":"Cubero, R. J., Jo, J., Marsili, M., Roudi, Y., &#38; Song, J. (2019). Statistical criticality arises in most informative representations. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">https://doi.org/10.1088/1742-5468/ab16c8</a>","ista":"Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. 2019. Statistical criticality arises in most informative representations. Journal of Statistical Mechanics: Theory and Experiment. 2019(6), 063402.","short":"R.J. Cubero, J. Jo, M. Marsili, Y. Roudi, J. Song, Journal of Statistical Mechanics: Theory and Experiment 2019 (2019).","chicago":"Cubero, Ryan J, Junghyo Jo, Matteo Marsili, Yasser Roudi, and Juyong Song. “Statistical Criticality Arises in Most Informative Representations.” <i>Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2019. <a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">https://doi.org/10.1088/1742-5468/ab16c8</a>.","ama":"Cubero RJ, Jo J, Marsili M, Roudi Y, Song J. Statistical criticality arises in most informative representations. <i>Journal of Statistical Mechanics: Theory and Experiment</i>. 2019;2019(6). doi:<a href=\"https://doi.org/10.1088/1742-5468/ab16c8\">10.1088/1742-5468/ab16c8</a>","ieee":"R. J. Cubero, J. Jo, M. Marsili, Y. Roudi, and J. Song, “Statistical criticality arises in most informative representations,” <i>Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2019, no. 6. IOP Publishing, 2019."},"_id":"7130","title":"Statistical criticality arises in most informative representations","date_created":"2019-11-26T22:36:09Z","publication_identifier":{"issn":["1742-5468"]},"publication_status":"published","fulldoi":"https://doi.org/10.1088/1742-5468/ab16c8","oa_version":"Preprint","oa":1,"article_processing_charge":"No","language":[{"iso":"eng"}],"year":"2019","type":"journal_article","publisher":"IOP Publishing","article_number":"063402","volume":2019,"arxiv":1,"abstract":[{"lang":"eng","text":"We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify the frequency with which different outcomes occur in a sample, as the variable carrying useful information on the generative process. The entropy of the frequency, that we call relevance, provides an upper bound to the number of informative bits. This differs from the entropy of the data, that we take as a measure of resolution. Samples that maximise relevance at a given resolution—that we call maximally informative samples—exhibit statistical criticality. In particular, Zipf's law arises at the optimal trade-off between resolution (i.e. compression) and relevance. As a byproduct, we derive a bound of the maximal number of parameters that can be estimated from a dataset, in the absence of prior knowledge on the generative model.\r\n\r\nFurthermore, we relate criticality to the statistical properties of the representation of the data generating process. We show that, as a consequence of the concentration property of the asymptotic equipartition property, representations that are maximally informative about the data generating process are characterised by an exponential distribution of energy levels. This arises from a principle of minimal entropy, that is conjugate of the maximum entropy principle in statistical mechanics. This explains why statistical criticality requires no parameter fine tuning in maximally informative samples."}],"extern":"1","intvolume":"      2019","date_updated":"2021-01-12T08:11:57Z"},{"citation":{"apa":"Peleg, N., Molnar, P., Burlando, P., &#38; Fatichi, S. (2019). Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator. <i>Journal of Hydrology</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jhydrol.2019.02.010\">https://doi.org/10.1016/j.jhydrol.2019.02.010</a>","short":"N. Peleg, P. Molnar, P. Burlando, S. Fatichi, Journal of Hydrology 571 (2019) 627–641.","ista":"Peleg N, Molnar P, Burlando P, Fatichi S. 2019. Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator. Journal of Hydrology. 571, 627–641.","mla":"Peleg, Nadav, et al. “Exploring Stochastic Climate Uncertainty in Space and Time Using a Gridded Hourly Weather Generator.” <i>Journal of Hydrology</i>, vol. 571, Elsevier, 2019, pp. 627–41, doi:<a href=\"https://doi.org/10.1016/j.jhydrol.2019.02.010\">10.1016/j.jhydrol.2019.02.010</a>.","chicago":"Peleg, Nadav, Peter Molnar, Paolo Burlando, and Simone Fatichi. “Exploring Stochastic Climate Uncertainty in Space and Time Using a Gridded Hourly Weather Generator.” <i>Journal of Hydrology</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jhydrol.2019.02.010\">https://doi.org/10.1016/j.jhydrol.2019.02.010</a>.","ieee":"N. Peleg, P. Molnar, P. Burlando, and S. Fatichi, “Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator,” <i>Journal of Hydrology</i>, vol. 571. Elsevier, pp. 627–641, 2019.","ama":"Peleg N, Molnar P, Burlando P, Fatichi S. Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator. <i>Journal of Hydrology</i>. 2019;571:627-641. doi:<a href=\"https://doi.org/10.1016/j.jhydrol.2019.02.010\">10.1016/j.jhydrol.2019.02.010</a>"},"scopus_import":"1","das_tickbox":"1","date_published":"2019-04-01T00:00:00Z","day":"01","article_type":"original","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1016/j.jhydrol.2019.02.010","keyword":["Weather generator","Stochastic downscaling","Climate change","Internal climate variability","Climate uncertainty","High-resolution rainfall model"],"quality_controlled":"1","publication":"Journal of Hydrology","month":"04","status":"public","author":[{"first_name":"Nadav","full_name":"Peleg, Nadav","last_name":"Peleg"},{"last_name":"Molnar","full_name":"Molnar, Peter","first_name":"Peter"},{"first_name":"Paolo","full_name":"Burlando, Paolo","last_name":"Burlando"},{"last_name":"Fatichi","first_name":"Simone","id":"cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6","full_name":"Fatichi, Simone"}],"volume":571,"page":"627-641","abstract":[{"text":"Exploring the effects of climate change on the hydrological response at the local scale requires climate data at high spatial and temporal resolutions. This is best achieved by generating downscaled ensembles of future climate variables derived from climate models. For this purpose we present a methodology to re-parameterize the AWE-GEN-2d model (Advanced WEather GENerator for a two-dimensional grid). The model simulates key meteorological variables needed by hydrological models and is particularly suitable to explore the effects of stochastic (natural) climatic uncertainty, which is fundamental for hydrological applications, especially at sub-kilometer and hourly scales. Factors of change for different climate statistics are calculated from climate model simulations of present and future climates and subsequently applied to the statistics derived from observations to re-parameterize AWE-GEN-2d. The model abilities in generating an ensemble of future climate variables for the transient period 2020–2089 is presented with examples of precipitation and near-surface air temperature fields from hourly to multi-annual scales for a small mountainous region in the Swiss Alps. The stochastic uncertainty is examined for present and future periods and for spatial scales from the RCM scale (12-km, daily) to 2-km demonstrating the potential use of AWE-GEN-2d outputs. At the RCM scale, model results yield a small increase in annual precipitation (4%) which is within the stochastic uncertainty range for present and future periods (7%). At the fine scale of 2-km, the increase in annual precipitation can exceed the stochastic uncertainty, but for less than 10% of the domain area. On the contrary, changes in annual near-surface air temperature exceed stochastic uncertainty both at the RCM and finer scales. Stochastic climate uncertainty was concluded to be very similar when comparing present and future periods and 12-km and 2-km scales. The benefits of using AWE-GEN-2d in hydrological climate change impact assessments are finally discussed.","lang":"eng"}],"extern":"1","date_updated":"2026-08-06T08:45:41Z","OA_type":"closed access","intvolume":"       571","year":"2019","language":[{"iso":"eng"}],"publisher":"Elsevier","type":"journal_article","publication_status":"published","oa_version":"None","fulldoi":"https://doi.org/10.1016/j.jhydrol.2019.02.010","article_processing_charge":"No","title":"Exploring stochastic climate uncertainty in space and time using a gridded hourly weather generator","_id":"22551","date_created":"2026-07-27T12:30:24Z","publication_identifier":{"eissn":["1879-2707"],"issn":["0022-1694"]}},{"year":"2018","language":[{"iso":"eng"}],"publisher":"Annals of Mathematics, Princeton U","type":"journal_article","extern":"1","intvolume":"       188","date_updated":"2021-01-12T08:19:10Z","volume":188,"page":"315-380","abstract":[{"text":"The classical Birkhoff conjecture claims that the boundary of a strictly convex integrable billiard table is necessarily an ellipse (or a circle as a special case). In this article we prove a complete local version of this conjecture: a small integrable perturbation of an ellipse must be an ellipse. This extends and completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains were considered. One of the crucial ideas in the proof is to extend action-angle coordinates for elliptic billiards into complex domains (with respect to the angle), and to thoroughly analyze the nature of their complex singularities. As an application, we are able to prove some spectral rigidity results for elliptic domains.","lang":"eng"}],"arxiv":1,"date_created":"2020-09-17T10:42:22Z","publication_identifier":{"issn":["0003-486X"]},"title":"On the local Birkhoff conjecture for convex billiards","_id":"8421","oa":1,"article_processing_charge":"No","publication_status":"published","oa_version":"Preprint","fulldoi":"https://doi.org/10.4007/annals.2018.188.1.6","date_published":"2018-07-01T00:00:00Z","external_id":{"arxiv":["1612.09194"]},"citation":{"ista":"Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex billiards. Annals of Mathematics. 188(1), 315–380.","apa":"Kaloshin, V., &#38; Sorrentino, A. (2018). On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>","short":"V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.","mla":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>, vol. 188, no. 1, Annals of Mathematics, Princeton U, 2018, pp. 315–80, doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>.","chicago":"Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture for Convex Billiards.” <i>Annals of Mathematics</i>. Annals of Mathematics, Princeton U, 2018. <a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">https://doi.org/10.4007/annals.2018.188.1.6</a>.","ieee":"V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex billiards,” <i>Annals of Mathematics</i>, vol. 188, no. 1. Annals of Mathematics, Princeton U, pp. 315–380, 2018.","ama":"Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards. <i>Annals of Mathematics</i>. 2018;188(1):315-380. doi:<a href=\"https://doi.org/10.4007/annals.2018.188.1.6\">10.4007/annals.2018.188.1.6</a>"},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.09194"}],"issue":"1","month":"07","status":"public","author":[{"first_name":"Vadim","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin"},{"first_name":"Alfonso","full_name":"Sorrentino, Alfonso","last_name":"Sorrentino"}],"quality_controlled":"1","publication":"Annals of Mathematics","doi":"10.4007/annals.2018.188.1.6","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"day":"01","article_type":"original"},{"publication_identifier":{"eissn":["1436-3259"],"issn":["1436-3240"]},"date_created":"2026-07-27T12:30:23Z","title":"Climate change and uncertainty assessment over a hydroclimatic transect of Michigan","_id":"22493","article_processing_charge":"No","oa_version":"None","fulldoi":"https://doi.org/10.1007/s00477-015-1097-2","publication_status":"published","publisher":"Springer Nature","type":"journal_article","year":"2015","language":[{"iso":"eng"}],"date_updated":"2026-08-12T13:55:28Z","OA_type":"closed access","intvolume":"        30","extern":"1","abstract":[{"lang":"eng","text":"Predictions of a warmer climate over the Great Lakes region due to global change generally agree on the magnitude of temperature changes, but precipitation projections exhibit dependence on which General Circulation Models and emission scenarios are chosen. To minimize model- and scenario-specific biases, we combined information provided by the 3rd phase of the Coupled Model Intercomparison Project database. Specifically, the results of 12 GCMs for three emission scenarios B1, A1B, and A2 were analyzed for mid- (2046–2065) and end-century (2081–2100) intervals, for six locations of a hydroclimatic transect of Michigan. As a result of Bayesian Weighted Averaging, total annual precipitation averaged over all locations and the three emission scenarios increases by 7 % (mid-)–10 % (end-century), as compared to the control period (1961–1990). The projected changes across seasons are non-uniform and precipitation decreases by 3 % (mid-)–5 % (end-) for the months of August and September are likely. Further, average temperature is very likely to increase by 2.02–2.85 °C by the mid-century and 2.58–4.73 °C by the end-century. Three types of non-additive uncertainty sources due to climate models, anthropogenic forcings, and climate internal variability are addressed. When compared to the emission uncertainty, the relative magnitudes of the uncertainty types for climate model ensemble and internal variability are 149 and 225 % for mean monthly precipitation, and they are respectively 127 and 123 % for mean monthly temperature. A decreasing trend of the frost days and an increasing trend of the growing season length are identified. Also, a significant increase in the magnitude and frequency of heavy rainfall events is projected, with relatively more pronounced changes for heavy hourly rainfall as compared to daily events. Quantifying the inherent natural uncertainty and projecting hourly-based extremes, the study results deliver useful information for water resource stakeholders interested in impacts of climate change on hydro-morphological processes."}],"volume":30,"page":"923-944","status":"public","month":"06","author":[{"last_name":"Kim","first_name":"Jongho","full_name":"Kim, Jongho"},{"full_name":"Ivanov, Valeriy Y.","first_name":"Valeriy Y.","last_name":"Ivanov"},{"full_name":"Fatichi, Simone","id":"cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6","first_name":"Simone","last_name":"Fatichi"}],"issue":"3","publication":"Stochastic Environmental Research and Risk Assessment","quality_controlled":"1","keyword":["Climate change","Weather generator","Stochastic downscaling","Uncertainty","CMIP3","Internal variability","Emission scenarios","Extreme indicators","The Great Lakes region"],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1007/s00477-015-1097-2","day":"16","article_type":"original","date_published":"2015-06-16T00:00:00Z","das_tickbox":"1","scopus_import":"1","citation":{"chicago":"Kim, Jongho, Valeriy Y. Ivanov, and Simone Fatichi. “Climate Change and Uncertainty Assessment over a Hydroclimatic Transect of Michigan.” <i>Stochastic Environmental Research and Risk Assessment</i>. Springer Nature, 2015. <a href=\"https://doi.org/10.1007/s00477-015-1097-2\">https://doi.org/10.1007/s00477-015-1097-2</a>.","apa":"Kim, J., Ivanov, V. Y., &#38; Fatichi, S. (2015). Climate change and uncertainty assessment over a hydroclimatic transect of Michigan. <i>Stochastic Environmental Research and Risk Assessment</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00477-015-1097-2\">https://doi.org/10.1007/s00477-015-1097-2</a>","ista":"Kim J, Ivanov VY, Fatichi S. 2015. Climate change and uncertainty assessment over a hydroclimatic transect of Michigan. Stochastic Environmental Research and Risk Assessment. 30(3), 923–944.","short":"J. Kim, V.Y. Ivanov, S. Fatichi, Stochastic Environmental Research and Risk Assessment 30 (2015) 923–944.","mla":"Kim, Jongho, et al. “Climate Change and Uncertainty Assessment over a Hydroclimatic Transect of Michigan.” <i>Stochastic Environmental Research and Risk Assessment</i>, vol. 30, no. 3, Springer Nature, 2015, pp. 923–44, doi:<a href=\"https://doi.org/10.1007/s00477-015-1097-2\">10.1007/s00477-015-1097-2</a>.","ama":"Kim J, Ivanov VY, Fatichi S. Climate change and uncertainty assessment over a hydroclimatic transect of Michigan. <i>Stochastic Environmental Research and Risk Assessment</i>. 2015;30(3):923-944. doi:<a href=\"https://doi.org/10.1007/s00477-015-1097-2\">10.1007/s00477-015-1097-2</a>","ieee":"J. Kim, V. Y. Ivanov, and S. Fatichi, “Climate change and uncertainty assessment over a hydroclimatic transect of Michigan,” <i>Stochastic Environmental Research and Risk Assessment</i>, vol. 30, no. 3. Springer Nature, pp. 923–944, 2015."}},{"date_published":"2014-09-15T00:00:00Z","external_id":{"pmid":["24418218"]},"das_tickbox":"1","scopus_import":"1","citation":{"mla":"Fatichi, Simone, et al. “Does Internal Climate Variability Overwhelm Climate Change Signals in Streamflow? The Upper Po and Rhone Basin Case Studies.” <i>Science of The Total Environment</i>, vol. 493, Elsevier, 2014, pp. 1171–82, doi:<a href=\"https://doi.org/10.1016/j.scitotenv.2013.12.014\">10.1016/j.scitotenv.2013.12.014</a>.","apa":"Fatichi, S., Rimkus, S., Burlando, P., &#38; Bordoy, R. (2014). Does internal climate variability overwhelm climate change signals in streamflow? The upper Po and Rhone basin case studies. <i>Science of The Total Environment</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.scitotenv.2013.12.014\">https://doi.org/10.1016/j.scitotenv.2013.12.014</a>","short":"S. Fatichi, S. Rimkus, P. Burlando, R. Bordoy, Science of The Total Environment 493 (2014) 1171–1182.","ista":"Fatichi S, Rimkus S, Burlando P, Bordoy R. 2014. Does internal climate variability overwhelm climate change signals in streamflow? The upper Po and Rhone basin case studies. Science of The Total Environment. 493, 1171–1182.","chicago":"Fatichi, Simone, S. Rimkus, P. Burlando, and R. Bordoy. “Does Internal Climate Variability Overwhelm Climate Change Signals in Streamflow? The Upper Po and Rhone Basin Case Studies.” <i>Science of The Total Environment</i>. Elsevier, 2014. <a href=\"https://doi.org/10.1016/j.scitotenv.2013.12.014\">https://doi.org/10.1016/j.scitotenv.2013.12.014</a>.","ama":"Fatichi S, Rimkus S, Burlando P, Bordoy R. Does internal climate variability overwhelm climate change signals in streamflow? The upper Po and Rhone basin case studies. <i>Science of The Total Environment</i>. 2014;493:1171-1182. doi:<a href=\"https://doi.org/10.1016/j.scitotenv.2013.12.014\">10.1016/j.scitotenv.2013.12.014</a>","ieee":"S. Fatichi, S. Rimkus, P. Burlando, and R. Bordoy, “Does internal climate variability overwhelm climate change signals in streamflow? The upper Po and Rhone basin case studies,” <i>Science of The Total Environment</i>, vol. 493. Elsevier, pp. 1171–1182, 2014."},"month":"09","status":"public","author":[{"last_name":"Fatichi","full_name":"Fatichi, Simone","id":"cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6","first_name":"Simone"},{"last_name":"Rimkus","first_name":"S.","full_name":"Rimkus, S."},{"last_name":"Burlando","first_name":"P.","full_name":"Burlando, P."},{"first_name":"R.","full_name":"Bordoy, R.","last_name":"Bordoy"}],"publication":"Science of The Total Environment","quality_controlled":"1","keyword":["Climate change","Hydrological modeling","Stochastic downscaling","Uncertainty","Water resources","Alps"],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1016/j.scitotenv.2013.12.014","day":"15","article_type":"original","publisher":"Elsevier","type":"journal_article","year":"2014","language":[{"iso":"eng"}],"OA_type":"closed access","intvolume":"       493","date_updated":"2026-08-12T14:17:26Z","extern":"1","abstract":[{"text":"Projections of climate change effects in streamflow are increasingly required to plan water management strategies. These projections are however largely uncertain due to the spread among climate model realizations, internal climate variability, and difficulties in transferring climate model results at the spatial and temporal scales required by catchment hydrology. A combination of a stochastic downscaling methodology and distributed hydrological modeling was used in the ACQWA project to provide projections of future streamflow (up to year 2050) for the upper Po and Rhone basins, respectively located in northern Italy and south-western Switzerland. Results suggest that internal (stochastic) climate variability is a fundamental source of uncertainty, typically comparable or larger than the projected climate change signal. Therefore, climate change effects in streamflow mean, frequency, and seasonality can be masked by natural climatic fluctuations in large parts of the analyzed regions. An exception to the overwhelming role of stochastic variability is represented by high elevation catchments fed by glaciers where streamflow is expected to be considerably reduced due to glacier retreat, with consequences appreciable in the main downstream rivers in August and September. Simulations also identify regions (west upper Rhone and Toce, Ticino river basins) where a strong precipitation increase in the February to April period projects streamflow beyond the range of natural climate variability during the melting season. This study emphasizes the importance of including internal climate variability in climate change analyses, especially when compared to the limited uncertainty that would be accounted for by few deterministic projections. The presented results could be useful in guiding more specific impact studies, although design or management decisions should be better based on reliability and vulnerability criteria as suggested by recent literature.","lang":"eng"}],"volume":493,"page":"1171-1182","publication_identifier":{"eissn":["1879-1026"],"issn":["0048-9697"]},"date_created":"2026-07-27T12:30:23Z","title":"Does internal climate variability overwhelm climate change signals in streamflow? The upper Po and Rhone basin case studies","_id":"22459","article_processing_charge":"No","oa_version":"None","pmid":1,"fulldoi":"https://doi.org/10.1016/j.scitotenv.2013.12.014","publication_status":"published"},{"intvolume":"        40","OA_type":"closed access","date_updated":"2026-08-12T14:05:37Z","extern":"1","abstract":[{"lang":"eng","text":"This study extends a stochastic downscaling methodology to generation of an ensemble of hourly time series of meteorological variables that express possible future climate conditions at a point-scale. The stochastic downscaling uses general circulation model (GCM) realizations and an hourly weather generator, the Advanced WEather GENerator (AWE-GEN). Marginal distributions of factors of change are computed for several climate statistics using a Bayesian methodology that can weight GCM realizations based on the model relative performance with respect to a historical climate and a degree of disagreement in projecting future conditions. A Monte Carlo technique is used to sample the factors of change from their respective marginal distributions. As a comparison with traditional approaches, factors of change are also estimated by averaging GCM realizations. With either approach, the derived factors of change are applied to the climate statistics inferred from historical observations to re-evaluate parameters of the weather generator. The re-parameterized generator yields hourly time series of meteorological variables that can be considered to be representative of future climate conditions. In this study, the time series are generated in an ensemble mode to fully reflect the uncertainty of GCM projections, climate stochasticity, as well as uncertainties of the downscaling procedure. Applications of the methodology in reproducing future climate conditions for the periods of 2000–2009, 2046–2065 and 2081–2100, using the period of 1962–1992 as the historical baseline are discussed for the location of Firenze (Italy). The inferences of the methodology for the period of 2000–2009 are tested against observations to assess reliability of the stochastic downscaling procedure in reproducing statistics of meteorological variables at different time scales."}],"page":"1841-1861","volume":40,"type":"journal_article","publisher":"Springer Nature","language":[{"iso":"eng"}],"year":"2013","article_processing_charge":"No","fulldoi":"https://doi.org/10.1007/s00382-012-1627-2","oa_version":"None","publication_status":"published","publication_identifier":{"issn":["0930-7575"],"eissn":["1432-0894"]},"date_created":"2026-07-27T12:30:23Z","_id":"22475","title":"Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series","das_tickbox":"1","scopus_import":"1","citation":{"chicago":"Fatichi, Simone, V. Y. Ivanov, and E. Caporali. “Assessment of a Stochastic Downscaling Methodology in Generating an Ensemble of Hourly Future Climate Time Series.” <i>Climate Dynamics</i>. Springer Nature, 2013. <a href=\"https://doi.org/10.1007/s00382-012-1627-2\">https://doi.org/10.1007/s00382-012-1627-2</a>.","mla":"Fatichi, Simone, et al. “Assessment of a Stochastic Downscaling Methodology in Generating an Ensemble of Hourly Future Climate Time Series.” <i>Climate Dynamics</i>, vol. 40, Springer Nature, 2013, pp. 1841–61, doi:<a href=\"https://doi.org/10.1007/s00382-012-1627-2\">10.1007/s00382-012-1627-2</a>.","ista":"Fatichi S, Ivanov VY, Caporali E. 2013. Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series. Climate Dynamics. 40, 1841–1861.","apa":"Fatichi, S., Ivanov, V. Y., &#38; Caporali, E. (2013). Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series. <i>Climate Dynamics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00382-012-1627-2\">https://doi.org/10.1007/s00382-012-1627-2</a>","short":"S. Fatichi, V.Y. Ivanov, E. Caporali, Climate Dynamics 40 (2013) 1841–1861.","ieee":"S. Fatichi, V. Y. Ivanov, and E. Caporali, “Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series,” <i>Climate Dynamics</i>, vol. 40. Springer Nature, pp. 1841–1861, 2013.","ama":"Fatichi S, Ivanov VY, Caporali E. Assessment of a stochastic downscaling methodology in generating an ensemble of hourly future climate time series. <i>Climate Dynamics</i>. 2013;40:1841-1861. doi:<a href=\"https://doi.org/10.1007/s00382-012-1627-2\">10.1007/s00382-012-1627-2</a>"},"date_published":"2013-04-01T00:00:00Z","keyword":["Stochastic downscaling","Weather generator","Uncertainty assessment","Firenze","Italy"],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1007/s00382-012-1627-2","article_type":"original","day":"01","author":[{"last_name":"Fatichi","first_name":"Simone","full_name":"Fatichi, Simone","id":"cf8e546b-a9b0-11f0-a43b-aa89ed1b56d6"},{"last_name":"Ivanov","full_name":"Ivanov, V. Y.","first_name":"V. Y."},{"first_name":"E.","full_name":"Caporali, E.","last_name":"Caporali"}],"status":"public","month":"04","publication":"Climate Dynamics","quality_controlled":"1"},{"intvolume":"       150","date_updated":"2021-01-12T08:19:53Z","extern":"1","volume":150,"citation":{"ama":"Kaloshin V. An extension of the Artin-Mazur theorem. <i>The Annals of Mathematics</i>. 1999;150(2):729-741. doi:<a href=\"https://doi.org/10.2307/121093\">10.2307/121093</a>","ieee":"V. Kaloshin, “An extension of the Artin-Mazur theorem,” <i>The Annals of Mathematics</i>, vol. 150, no. 2. JSTOR, pp. 729–741, 1999.","short":"V. Kaloshin, The Annals of Mathematics 150 (1999) 729–741.","apa":"Kaloshin, V. (1999). An extension of the Artin-Mazur theorem. <i>The Annals of Mathematics</i>. JSTOR. <a href=\"https://doi.org/10.2307/121093\">https://doi.org/10.2307/121093</a>","ista":"Kaloshin V. 1999. An extension of the Artin-Mazur theorem. The Annals of Mathematics. 150(2), 729–741.","mla":"Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” <i>The Annals of Mathematics</i>, vol. 150, no. 2, JSTOR, 1999, pp. 729–41, doi:<a href=\"https://doi.org/10.2307/121093\">10.2307/121093</a>.","chicago":"Kaloshin, Vadim. “An Extension of the Artin-Mazur Theorem.” <i>The Annals of Mathematics</i>. JSTOR, 1999. <a href=\"https://doi.org/10.2307/121093\">https://doi.org/10.2307/121093</a>."},"page":"729-741","publisher":"JSTOR","type":"journal_article","date_published":"1999-09-01T00:00:00Z","year":"1999","language":[{"iso":"eng"}],"article_processing_charge":"No","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.2307/121093","day":"01","oa_version":"None","fulldoi":"https://doi.org/10.2307/121093","article_type":"original","publication_status":"published","month":"09","status":"public","publication_identifier":{"issn":["0003-486X"]},"author":[{"last_name":"Kaloshin","first_name":"Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628","full_name":"Kaloshin, Vadim"}],"date_created":"2020-09-18T10:50:28Z","issue":"2","publication":"The Annals of Mathematics","title":"An extension of the Artin-Mazur theorem","_id":"8526","quality_controlled":"1"}]