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UID:20260602T221221EDT-4871mWeH4R@132.216.98.100
DTSTAMP:20260603T021221Z
DESCRIPTION:Title: Extreme eigenvalues of random d -regular graphs.\n\nAbst
 ract: Extremal eigenvalues of graphs are of particular interest in theoret
 ical computer science and combinatorics. In particular\, the spectral gap\
 , the gap between the first and second largest eigenvalues\, measures the 
 expanding property of the graph. In this talk\, I will focus on random d-r
 egular graphs. I’ll first explain some conjectures on the extremal eigenva
 lue distributions of adjacency matrices of random d-regular graphs\; some 
 have been solved\, some are still widely open. In the second part of the t
 alk\, I will give a new proof of Alon’s second eigenvalue conjecture that 
 with high probability\, the second eigenvalue of a random d-regular graph 
 is bounded by 2√ d − 1+o(1)\, where we can show that the error term is pol
 ynomially small in the size of the graph. This is based on a joint work wi
 th Horng-Tzer Yau.\n
DTSTART:20220606T160000Z
DTEND:20220606T170000Z
SUMMARY:Jiaoyang Huang (Courant Institute)
URL:/mathstat/channels/event/jiaoyang-huang-courant-in
 stitute-339748
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