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SUMMARY:Spectral radii of sparse random matrices - Antti Knowles (Geneva)
DTSTART:20170307T151500Z
DTEND:20170307T161500Z
UID:TALK71497@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:We establish bounds on the spectral radii for a large class of
 \nsparse random matrices\, which includes the adjacency matrices of\ninhom
 ogeneous Erd\\H{o}s-R\\'enyi graphs. For the Erd\\H{o}s-R\\'enyi graph $G(
 n\,d/n)$\, our results imply that the smallest and second-largest\neigenva
 lues of the adjacency matrix converge to the edges of the support of the a
 symptotic eigenvalue distribution provided that $d \\gg \\log n$. This est
 ablishes a crossover in the behaviour of the extremal eigenvalues around $
 d \\sim \\log n$. Our results also apply to non-Hermitian sparse random ma
 trices\, corresponding to adjacency matrices of directed graphs. Joint wor
 k with Florent Benaych-Georges and Charles Bordenave.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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