[{"language":[{"iso":"eng"}],"publication":"Bernoulli","oa_version":"Preprint","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"month":"05","main_file_link":[{"url":"https://arxiv.org/abs/2112.12093","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","date_published":"2023-05-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["1350-7265"]},"oa":1,"page":"1063-1079","quality_controlled":"1","ec_funded":1,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","article_type":"original","_id":"12707","scopus_import":"1","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Xu, Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"issue":"2","publication_status":"published","article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2023-03-05T23:01:05Z","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","intvolume":"        29","volume":29,"date_updated":"2023-10-04T10:21:07Z","year":"2023","citation":{"ieee":"L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” <i>Bernoulli</i>, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.","chicago":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2023. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>.","apa":"Erdös, L., &#38; Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>","ama":"Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. 2023;29(2):1063-1079. doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","mla":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>."},"isi":1,"external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"doi":"10.3150/22-BEJ1490","arxiv":1,"day":"01","abstract":[{"lang":"eng","text":"We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail."}]},{"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2007.11998"}],"date_published":"2022-05-01T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["1350-7265"]},"language":[{"iso":"eng"}],"keyword":["Statistics and Probability"],"publication":"Bernoulli","month":"05","oa_version":"Preprint","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"acknowledgement":"C.F. and P.G. thank FCT/Portugal for support through the project UID/MAT/04459/2013.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this work has been done, and the European research and innovative programme No. 715734 for the kind hospitality.","volume":28,"isi":1,"external_id":{"isi":["000766619100025"],"arxiv":["2007.11998"]},"date_updated":"2023-08-04T10:27:35Z","citation":{"ama":"Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. <i>Bernoulli</i>. 2022;28(2):1340-1381. doi:<a href=\"https://doi.org/10.3150/21-bej1390\">10.3150/21-bej1390</a>","apa":"Franceschini, C., Gonçalves, P., &#38; Sau, F. (2022). Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/21-bej1390\">https://doi.org/10.3150/21-bej1390</a>","chicago":"Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2022. <a href=\"https://doi.org/10.3150/21-bej1390\">https://doi.org/10.3150/21-bej1390</a>.","ieee":"C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” <i>Bernoulli</i>, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.","mla":"Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” <i>Bernoulli</i>, vol. 28, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:<a href=\"https://doi.org/10.3150/21-bej1390\">10.3150/21-bej1390</a>.","short":"C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381.","ista":"Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381."},"year":"2022","abstract":[{"lang":"eng","text":"We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle."}],"doi":"10.3150/21-bej1390","arxiv":1,"day":"01","page":"1340-1381","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Bernoulli Society for Mathematical Statistics and Probability","author":[{"last_name":"Franceschini","first_name":"Chiara","full_name":"Franceschini, Chiara"},{"last_name":"Gonçalves","first_name":"Patrícia","full_name":"Gonçalves, Patrícia"},{"last_name":"Sau","first_name":"Federico","full_name":"Sau, Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425"}],"issue":"2","_id":"12281","scopus_import":"1","title":"Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics","intvolume":"        28","publication_status":"published","article_processing_charge":"No","department":[{"_id":"JaMa"}],"date_created":"2023-01-16T10:03:04Z"}]