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Central Limit Theorems for the Energy Density in the High Temperature phase of the Sherrington Kirkpatrick Model

Mathematical Physics & Probability

Speaker: Nick Crawford, UC Berkeley
Location: 1147 MSB
Start time: Wed, May 7 2008, 4:10PM

This talk regards quenched central limit theorems for macroscopic observables in the High temperature phase of the Sherrinton-Kirkpatrick Model of Spin Glasses. Comets and Neveau, and independently Chatterjee, showed that if there is no external field, then the energy density satisfies a quenched CLT in the limit as the volume tends to infinity. The general case was left open and it was not clear how to proceed. We show one method to resolve this problem, applying a combination of the cavity method and Stein's method, a powerful quantitative tool for proving CLT's. Based on joint work w/ Sourav Chatterjee.