We will have our last talk of the year tomorrow, at 3pm in Fields 210. The speaker is Elizabeth Collins-Woodfin from McGill University.
Title: Bipartite spherical spin glass at critical temperature (with a random matrix detour)
Abstract: One of the fascinating phenomena of spin glasses is the dramatic
change in behavior that occurs between the high and low temperature
regimes. The free energy of the spherical Sherrington-Kirkpatrick (SSK)
model, for example, has Gaussian fluctuations at high temperature, but
Tracy-Widom fluctuations at low temperature. A similar phenomenon holds
for the bipartite SSK model, and we show that, when the temperature is
within a small window around the critical temperature, the free energy
fluctuations converge to an independent sum of Gaussian and Tracy-Widom
random variables (joint work with Han Le). Our work follows two recent
papers that proved similar results for the SSK model (by Landon and by
Johnstone, Klochkov, Onatski, Pavlyshyn).
Analyzing the free
energy fluctuations of bipartite SSK at critical temperature requires a
variety of tools including classical random matrix results, contour
integral techniques, and a CLT for the log-characteristic polynomial of
Laguerre (Wishart) random matrices, evaluated near the spectral edge.
This last ingredient was not present in the literature when we began our
project, so I will also discuss our proof of this CLT, which has other
applications separate from bipartite spin glasses.