[{"isi":1,"type":"journal_article","author":[{"id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J","last_name":"Campbell","full_name":"Campbell, Andrew J"},{"last_name":"O’Rourke","full_name":"O’Rourke, Sean","first_name":"Sean"}],"corr_author":"1","page":"933-973","article_type":"original","_id":"13975","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2023-08-06T22:01:13Z","supplementarymaterial":"yes","article_processing_charge":"Yes (via OA deal)","status":"public","oa":1,"day":"01","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","date_published":"2024-03-01T00:00:00Z","date_updated":"2026-10-16T08:30:34Z","month":"03","dataavailabilitystatement":"All data generated or analyzed during this study are included in this published article.","researchdata_availability":"yes (supplementary data)","abstract":[{"text":"We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln  converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure.","lang":"eng"}],"file_date_updated":"2024-07-22T09:41:21Z","intvolume":"        37","acknowledgement":"The first author thanks Yizhe Zhu for pointing out reference [30]. We thank David Renfrew for comments on an earlier draft. We thank the anonymous referee for a careful reading and helpful comments.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","publisher":"Springer Nature","year":"2024","volume":37,"language":[{"iso":"eng"}],"scopus_import":"1","citation":{"ista":"Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 37, 933–973.","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” <i>Journal of Theoretical Probability</i>, vol. 37. Springer Nature, pp. 933–973, 2024.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>.","ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. 2024;37:933-973. doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>","apa":"Campbell, A. J., &#38; O’Rourke, S. (2024). Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>, vol. 37, Springer Nature, 2024, pp. 933–73, doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>.","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973."},"oa_version":"Published Version","file":[{"date_created":"2024-07-22T09:41:21Z","success":1,"access_level":"open_access","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_id":"17300","file_size":555070,"checksum":"f7793d313104c70422140c5e6494c779","date_updated":"2024-07-22T09:41:21Z","file_name":"2024_JourTheorProbab_Campbell.pdf"}],"fulldoi":"https://doi.org/10.1007/s10959-023-01275-4","arxiv":1,"department":[{"_id":"LaEr"}],"has_accepted_license":"1","ddc":["510"],"doi":"10.1007/s10959-023-01275-4","external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"title":"Spectrum of Lévy–Khintchine random laplacian matrices","license":"https://creativecommons.org/licenses/by/4.0/","das_tickbox":"1","publication_status":"published","publication":"Journal of Theoretical Probability","publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]}}]