Yu Cheng

Critical-Window Fluctuations and Disorder Universality for the Sherrington--Kirkpatrick Model

We establish free-energy fluctuation limits for the Ising Sherrington--Kirkpatrick model in the nonzero parts of its critical window. For fixed $b\ne0$ and $\beta_N=1+bN^{-1/3}\sqrt{\log N}$, our main Gaussian orthogonal ensemble (GOE) result is \[ \sqrt{\frac6{\log N}}\left(F_{N,\beta_N}-N\,\mathrm{FE}(\beta_N)+\frac{...