{"title":"随机双曲面上拉普拉斯的确定性","authors":"Frédéric Naud","doi":"10.1007/s11854-023-0334-8","DOIUrl":null,"url":null,"abstract":"<p>For sequences (<i>X</i><sub><i>j</i></sub>) of random closed hyperbolic surfaces with volume Vol(<i>X</i><sub><i>j</i></sub>) tending to infinity, we prove that there exists a universal constant <i>E</i> > 0 such that for all <i>ϵ</i> > 0, the regularized determinant of the Laplacian satisfies </p><span>$${{\\log \\det ({\\Delta _{{X_j}}})} \\over {{\\rm{Vol}}({X_j})}} \\in [E -\\epsilon ,E +\\epsilon]$$</span><p> with high probability as <i>j</i> → +⋡. This result holds for various models of random surfaces, including the Weil–Petersson model.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"87 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Determinants of Laplacians on random hyperbolic surfaces\",\"authors\":\"Frédéric Naud\",\"doi\":\"10.1007/s11854-023-0334-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For sequences (<i>X</i><sub><i>j</i></sub>) of random closed hyperbolic surfaces with volume Vol(<i>X</i><sub><i>j</i></sub>) tending to infinity, we prove that there exists a universal constant <i>E</i> > 0 such that for all <i>ϵ</i> > 0, the regularized determinant of the Laplacian satisfies </p><span>$${{\\\\log \\\\det ({\\\\Delta _{{X_j}}})} \\\\over {{\\\\rm{Vol}}({X_j})}} \\\\in [E -\\\\epsilon ,E +\\\\epsilon]$$</span><p> with high probability as <i>j</i> → +⋡. This result holds for various models of random surfaces, including the Weil–Petersson model.</p>\",\"PeriodicalId\":502135,\"journal\":{\"name\":\"Journal d'Analyse Mathématique\",\"volume\":\"87 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal d'Analyse Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11854-023-0334-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal d'Analyse Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11854-023-0334-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Determinants of Laplacians on random hyperbolic surfaces
For sequences (Xj) of random closed hyperbolic surfaces with volume Vol(Xj) tending to infinity, we prove that there exists a universal constant E > 0 such that for all ϵ > 0, the regularized determinant of the Laplacian satisfies
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
