[{"file_date_updated":"2025-11-04T07:34:05Z","PlanS_conform":"1","type":"journal_article","DOAJ_listed":"1","date_updated":"2025-12-01T15:08:54Z","abstract":[{"lang":"eng","text":"In this paper we derive estimates for the Hessian of the logarithm (log-Hessian) for solutions to the heat equation. For initial data in the form of log-Lipschitz perturbation of strongly log-concave measures, the log-Hessian admits an explicit, uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant of a transport map pushing forward the standard Gaussian to a measure in this class. On the other hand, we show that assuming only fast decay of the tails of the initial datum does not suffice to guarantee uniform log-Hessian upper bounds."}],"publication":"Electronic Communications in Probability","date_created":"2025-11-02T23:01:35Z","publication_identifier":{"eissn":["1083-589X"]},"oa":1,"has_accepted_license":"1","article_type":"original","OA_place":"publisher","title":"Heat flow, log-concavity, and Lipschitz transport maps","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"gold","scopus_import":"1","acknowledgement":"This research was funded in part by the Austrian Science Fund (FWF) project 10.55776/F65 and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101034413. The authors thank Professors Jean Dolbeault, Jan Maas, and Nikita Simonov for many useful comments, and Professors Kazuhiro Ishige, Asuka Takatsu, and Yair Shenfeld for inspiring interactions.","status":"public","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"creator":"dernst","file_size":278078,"date_updated":"2025-11-04T07:34:05Z","file_name":"2025_ElectronJourProbab_Brigati.pdf","file_id":"20596","date_created":"2025-11-04T07:34:05Z","checksum":"67858edbd74658fe38955fa1216f2f18","relation":"main_file","content_type":"application/pdf","access_level":"open_access","success":1}],"citation":{"ista":"Brigati G, Pedrotti F. 2025. Heat flow, log-concavity, and Lipschitz transport maps. Electronic Communications in Probability. 30, 71.","chicago":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>.","mla":"Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>, vol. 30, 71, Institute of Mathematical Statistics, 2025, doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>.","short":"G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025).","apa":"Brigati, G., &#38; Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-ECP717\">https://doi.org/10.1214/25-ECP717</a>","ama":"Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps. <i>Electronic Communications in Probability</i>. 2025;30. doi:<a href=\"https://doi.org/10.1214/25-ECP717\">10.1214/25-ECP717</a>","ieee":"G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport maps,” <i>Electronic Communications in Probability</i>, vol. 30. Institute of Mathematical Statistics, 2025."},"arxiv":1,"oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"17353"}]},"month":"09","corr_author":"1","department":[{"_id":"JaMa"}],"publication_status":"published","ec_funded":1,"day":"25","doi":"10.1214/25-ECP717","volume":30,"intvolume":"        30","isi":1,"author":[{"first_name":"Giovanni","last_name":"Brigati","id":"63ff57e8-1fbb-11ee-88f2-f558ffc59cf1","full_name":"Brigati, Giovanni"},{"last_name":"Pedrotti","full_name":"Pedrotti, Francesco","id":"d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c","first_name":"Francesco"}],"_id":"20591","external_id":{"arxiv":["2404.15205"],"isi":["001611557000018"]},"year":"2025","article_number":"71","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"call_identifier":"H2020","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c"}],"publisher":"Institute of Mathematical Statistics","ddc":["500"],"article_processing_charge":"Yes","date_published":"2025-09-25T00:00:00Z"},{"arxiv":1,"oa_version":"Published Version","language":[{"iso":"eng"}],"quality_controlled":"1","month":"11","corr_author":"1","day":"24","ec_funded":1,"doi":"10.1214/24-ECP639","department":[{"_id":"MaKw"}],"publication_status":"published","acknowledgement":"Research supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101034413.\r\nThe authors wish to thank Ross Pinsky for his comments on an earlier version of the paper, and for bringing reference [12] to our attention. The authors are grateful to the anonymous referees for their helpful comments and suggestions.","scopus_import":"1","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2311.16631","open_access":"1"}],"citation":{"chicago":"Anastos, Michael, Sahar Diskin, Dor Elboim, and Michael Krivelevich. “Climbing up a Random Subgraph of the Hypercube.” <i>Electronic Communications in Probability</i>. Duke University Press, 2024. <a href=\"https://doi.org/10.1214/24-ECP639\">https://doi.org/10.1214/24-ECP639</a>.","mla":"Anastos, Michael, et al. “Climbing up a Random Subgraph of the Hypercube.” <i>Electronic Communications in Probability</i>, vol. 29, 70, Duke University Press, 2024, doi:<a href=\"https://doi.org/10.1214/24-ECP639\">10.1214/24-ECP639</a>.","short":"M. Anastos, S. Diskin, D. Elboim, M. Krivelevich, Electronic Communications in Probability 29 (2024).","ista":"Anastos M, Diskin S, Elboim D, Krivelevich M. 2024. Climbing up a random subgraph of the hypercube. Electronic Communications in Probability. 29, 70.","ieee":"M. Anastos, S. Diskin, D. Elboim, and M. Krivelevich, “Climbing up a random subgraph of the hypercube,” <i>Electronic Communications in Probability</i>, vol. 29. Duke University Press, 2024.","apa":"Anastos, M., Diskin, S., Elboim, D., &#38; Krivelevich, M. (2024). Climbing up a random subgraph of the hypercube. <i>Electronic Communications in Probability</i>. Duke University Press. <a href=\"https://doi.org/10.1214/24-ECP639\">https://doi.org/10.1214/24-ECP639</a>","ama":"Anastos M, Diskin S, Elboim D, Krivelevich M. Climbing up a random subgraph of the hypercube. <i>Electronic Communications in Probability</i>. 2024;29. doi:<a href=\"https://doi.org/10.1214/24-ECP639\">10.1214/24-ECP639</a>"},"file":[{"success":1,"access_level":"open_access","content_type":"application/pdf","relation":"main_file","checksum":"307a9d049325e6ca9bfe8b4a1f275983","date_created":"2024-12-16T07:33:34Z","file_id":"18657","file_name":"2024_ElectrCommProbability_Anastos.pdf","date_updated":"2024-12-16T07:33:34Z","file_size":530169,"creator":"dernst"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"oa":1,"has_accepted_license":"1","OA_place":"repository","article_type":"original","OA_type":"gold","title":"Climbing up a random subgraph of the hypercube","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","file_date_updated":"2024-12-16T07:33:34Z","date_updated":"2025-09-09T11:46:53Z","DOAJ_listed":"1","type":"journal_article","abstract":[{"lang":"eng","text":"Let Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is an increasing path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is obtained by switching some zero coordinate in vi to a one coordinate in vi+1.\r\nForm a random subgraph Qdp by retaining each edge in E(Qd) independently with probability p. We show that there is a phase transition with respect to the length of a longest increasing path around p=ed. Let α be a constant and let p=αd. When α<e, then there exists a δ∈[0,1) such that whp a longest increasing path in Qdp is of length at most δd. On the other hand, when α>e, whp there is a path of length d−2 in Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the all-zero and all-one vertices percolate or not."}],"publication_identifier":{"eissn":["1083-589X"]},"publication":"Electronic Communications in Probability","date_created":"2024-12-15T23:01:51Z","article_processing_charge":"Yes","date_published":"2024-11-24T00:00:00Z","article_number":"70","year":"2024","publisher":"Duke University Press","project":[{"_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","grant_number":"101034413","name":"IST-BRIDGE: International postdoctoral program","call_identifier":"H2020"}],"ddc":["510"],"isi":1,"author":[{"first_name":"Michael","last_name":"Anastos","id":"0b2a4358-bb35-11ec-b7b9-e3279b593dbb","full_name":"Anastos, Michael"},{"first_name":"Sahar","last_name":"Diskin","full_name":"Diskin, Sahar"},{"first_name":"Dor","last_name":"Elboim","full_name":"Elboim, Dor"},{"full_name":"Krivelevich, Michael","last_name":"Krivelevich","first_name":"Michael"}],"_id":"18655","external_id":{"isi":["001356019700001"],"arxiv":["2311.16631"]},"volume":29,"intvolume":"        29"},{"abstract":[{"lang":"eng","text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices."}],"publication_identifier":{"eissn":["1083-589X"]},"publication":"Electronic Communications in Probability","date_created":"2023-02-26T23:01:01Z","file_date_updated":"2023-02-27T09:43:27Z","date_updated":"2025-04-14T07:44:00Z","type":"journal_article","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","oa":1,"has_accepted_license":"1","status":"public","file":[{"file_name":"2023_ElectCommProbability_Dubach.pdf","file_id":"12692","date_created":"2023-02-27T09:43:27Z","file_size":479105,"creator":"dernst","date_updated":"2023-02-27T09:43:27Z","success":1,"access_level":"open_access","relation":"main_file","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","content_type":"application/pdf"}],"citation":{"ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023."},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","scopus_import":"1","corr_author":"1","month":"02","ec_funded":1,"day":"08","doi":"10.1214/23-ECP516","department":[{"_id":"LaEr"}],"publication_status":"published","arxiv":1,"oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}],"intvolume":"        28","volume":28,"external_id":{"arxiv":["2108.13694"],"isi":["000950650200005"]},"_id":"12683","isi":1,"author":[{"orcid":"0000-0001-6892-8137","first_name":"Guillaume","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"}],"publisher":"Institute of Mathematical Statistics","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"ddc":["510"],"year":"2023","date_published":"2023-02-08T00:00:00Z","article_processing_charge":"No","page":"1-13"},{"ddc":["510"],"publisher":"Institute of Mathematical Statistics","project":[{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"}],"year":"2023","date_published":"2023-05-05T00:00:00Z","page":"1-12","article_processing_charge":"No","intvolume":"        28","volume":28,"external_id":{"isi":["001042025400001"]},"_id":"13145","author":[{"first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Eugene","full_name":"Lytvynov, Eugene","last_name":"Lytvynov"}],"isi":1,"citation":{"apa":"Dello Schiavo, L., &#38; Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>","ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. 2023;28:1-12. doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023.","ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12.","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>.","short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12.","chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>."},"file":[{"file_name":"2023_ElectronCommProbability_Schiavo.pdf","file_id":"13152","date_created":"2023-06-19T09:37:40Z","file_size":271434,"creator":"dernst","date_updated":"2023-06-19T09:37:40Z","success":1,"access_level":"open_access","relation":"main_file","checksum":"4a543fe4b3f9e747cc52167c17bfb524","content_type":"application/pdf"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"status":"public","acknowledgement":"Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208.","scopus_import":"1","doi":"10.1214/23-ECP528","day":"05","publication_status":"published","department":[{"_id":"JaMa"}],"month":"05","corr_author":"1","oa_version":"Published Version","quality_controlled":"1","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1083-589X"]},"publication":"Electronic Communications in Probability","date_created":"2023-06-18T22:00:48Z","abstract":[{"text":"We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.","lang":"eng"}],"date_updated":"2025-04-14T12:59:08Z","type":"journal_article","file_date_updated":"2023-06-19T09:37:40Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","article_type":"original","oa":1,"has_accepted_license":"1"}]