[{"external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"date_created":"2023-08-06T22:01:13Z","ddc":["510"],"abstract":[{"lang":"eng","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."}],"article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","arxiv":1,"day":"01","publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]},"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).","scopus_import":"1","file":[{"file_name":"2024_JourTheorProbab_Campbell.pdf","relation":"main_file","date_created":"2024-07-22T09:41:21Z","checksum":"f7793d313104c70422140c5e6494c779","access_level":"open_access","creator":"dernst","file_size":555070,"file_id":"17300","success":1,"content_type":"application/pdf","date_updated":"2024-07-22T09:41:21Z"}],"file_date_updated":"2024-07-22T09:41:21Z","date_updated":"2024-07-22T09:41:42Z","_id":"13975","type":"journal_article","page":"933-973","oa":1,"date_published":"2024-03-01T00:00:00Z","publication":"Journal of Theoretical Probability","publication_status":"published","corr_author":"1","citation":{"short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973.","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>","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>.","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.","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>","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>."},"isi":1,"intvolume":"        37","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"quality_controlled":"1","status":"public","doi":"10.1007/s10959-023-01275-4","department":[{"_id":"LaEr"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"title":"Spectrum of Lévy–Khintchine random laplacian matrices","month":"03","publisher":"Springer Nature","year":"2024","volume":37,"author":[{"id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J","full_name":"Campbell, Andrew J","last_name":"Campbell"},{"last_name":"O’Rourke","first_name":"Sean","full_name":"O’Rourke, Sean"}],"article_processing_charge":"Yes (via OA deal)"}]