BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//prob.tw//NTU Seminars V2//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
UID:2024-07-29-yau-horng-tzer-spectral-statistics-of-random-regular-graphs@seminars.prob.tw
DTSTAMP:20261014T103701Z
DTSTART:20240729T060000Z
DTEND:20240729T073000Z
SUMMARY:Spectral Statistics of Random Regular Graphs
DESCRIPTION:姚鴻澤 (Yau\, Horng-Tzer)\nIn this lecture\, we will review recent works regarding spectral statistics of the normalized adjacency matrices of random $d$-regular graphs on $N$ vertices. Denote their eigenvalues by $\\lambda_1 = d/\\sqrt{d-1} \\geq \\lambda_2 \\geq \\dots \\geq \\lambda_N$\, and let $\\gamma_i$ be the classical location of the $i$-th eigenvalue under the Kesten-McKay law. Our main result asserts that for any $d \\geq 3$ the optimal eigenvalue rigidity holds in the sense that $$|\\lambda_i − \\gamma_i| \\leq \\frac{N^{o_N(1)}}{N^{2/3}(\\min \\{ i\, N − i + 1 \\})^{1/3} }\, \\quad \\forall i \\in \\{ 2\, 3\, \\dots\, N \\}$$ with probability $1 − N^{−1+o_N(1)}$. In particular\, the characteristic $N^{−2/3}$ fluctuations for Tracy-Widom law is established for the second largest eigenvalue. Furthermore\, for $d \\geq N \\epsilon$ for any $\\epsilon > 0$ fixed\, the extremal eigenvalues obey the Tracy-Widom law. This is a joint work with Jiaoyang Huang and Theo McKenzie.
LOCATION:台大次震宇宙館 515 室
URL:http://127.0.0.1:8123/?event=2024-07-29-yau-horng-tzer-spectral-statistics-of-random-regular-graphs
END:VEVENT
END:VCALENDAR