{"publication_status":"published","oa_version":"Published Version","publication":"Electronic Journal of Probability","_id":"20046","DOAJ_listed":"1","department":[{"_id":"LaEr"}],"date_updated":"2025-07-23T08:38:00Z","doi":"10.1214/25-ejp1366","corr_author":"1","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","author":[{"id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","last_name":"Campbell","first_name":"Andrew J","full_name":"Campbell, Andrew J"},{"first_name":"Kyle","last_name":"Luh","full_name":"Luh, Kyle"},{"full_name":"O’Rourke, Sean","first_name":"Sean","last_name":"O’Rourke"},{"first_name":"Santiago","last_name":"Arenas-Velilla","full_name":"Arenas-Velilla, Santiago"},{"last_name":"Perez-Abreu","first_name":"Victor","full_name":"Perez-Abreu, Victor"}],"intvolume":"        30","article_type":"original","page":"1-52","day":"27","language":[{"iso":"eng"}],"OA_place":"publisher","has_accepted_license":"1","publication_identifier":{"eissn":["1083-6489"]},"file_date_updated":"2025-07-23T08:35:53Z","article_processing_charge":"Yes","OA_type":"gold","acknowledgement":"The authors thank Santiago Arenas-Velilla and Victor Pérez-Abreu for comments on an earlier draft of this manuscript and for contributing Appendix A. The authors also thank Yan Fyodorov for providing useful references.\r\nA. Campbell was partially supported by the European Research Council Grant No. 101020331. K. Luh was supported in part by the Ralph E. Powe Junior Faculty Enhancement Award and Simons Foundation Grant MP-TSM-00001988. S. O’Rourke has been supported in part by NSF CAREER grant DMS-2143142. ","month":"06","external_id":{"arxiv":["2211.17175"]},"ec_funded":1,"date_published":"2025-06-27T00:00:00Z","title":"Extreme eigenvalues of Laplacian random matrices with Gaussian entries","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"abstract":[{"text":"A Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We investigate the limiting distribution of the largest eigenvalues of a Laplacian random matrix with Gaussian entries. Unlike many classical matrix ensembles, this random matrix model contains dependent entries. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics. In particular, after properly shifting and scaling, we show that the largest eigenvalue converges to the Gumbel distribution as the dimension of the matrix tends to infinity. While the largest diagonal entry is also shown to have Gumbel fluctuations, there is a rather surprising difference between its deterministic centering term and the centering term required for the largest eigenvalues.","lang":"eng"}],"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"arxiv":1,"file":[{"file_size":580591,"checksum":"a7a9f2bb7a6295786c16d4c7bd612621","date_created":"2025-07-23T08:35:53Z","relation":"main_file","success":1,"file_name":"2025_ElectronJourProbab_Campbell.pdf","file_id":"20069","content_type":"application/pdf","date_updated":"2025-07-23T08:35:53Z","creator":"dernst","access_level":"open_access"}],"status":"public","year":"2025","citation":{"mla":"Campbell, Andrew J., et al. “Extreme Eigenvalues of Laplacian Random Matrices with Gaussian Entries.” <i>Electronic Journal of Probability</i>, vol. 30, Institute of Mathematical Statistics, 2025, pp. 1–52, doi:<a href=\"https://doi.org/10.1214/25-ejp1366\">10.1214/25-ejp1366</a>.","short":"A.J. Campbell, K. Luh, S. O’Rourke, S. Arenas-Velilla, V. Perez-Abreu, Electronic Journal of Probability 30 (2025) 1–52.","ama":"Campbell AJ, Luh K, O’Rourke S, Arenas-Velilla S, Perez-Abreu V. Extreme eigenvalues of Laplacian random matrices with Gaussian entries. <i>Electronic Journal of Probability</i>. 2025;30:1-52. doi:<a href=\"https://doi.org/10.1214/25-ejp1366\">10.1214/25-ejp1366</a>","chicago":"Campbell, Andrew J, Kyle Luh, Sean O’Rourke, Santiago Arenas-Velilla, and Victor Perez-Abreu. “Extreme Eigenvalues of Laplacian Random Matrices with Gaussian Entries.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-ejp1366\">https://doi.org/10.1214/25-ejp1366</a>.","apa":"Campbell, A. J., Luh, K., O’Rourke, S., Arenas-Velilla, S., &#38; Perez-Abreu, V. (2025). Extreme eigenvalues of Laplacian random matrices with Gaussian entries. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-ejp1366\">https://doi.org/10.1214/25-ejp1366</a>","ista":"Campbell AJ, Luh K, O’Rourke S, Arenas-Velilla S, Perez-Abreu V. 2025. Extreme eigenvalues of Laplacian random matrices with Gaussian entries. Electronic Journal of Probability. 30, 1–52.","ieee":"A. J. Campbell, K. Luh, S. O’Rourke, S. Arenas-Velilla, and V. Perez-Abreu, “Extreme eigenvalues of Laplacian random matrices with Gaussian entries,” <i>Electronic Journal of Probability</i>, vol. 30. Institute of Mathematical Statistics, pp. 1–52, 2025."},"publisher":"Institute of Mathematical Statistics","volume":30,"date_created":"2025-07-21T08:06:18Z","type":"journal_article"}