Jinho Baik

Fluctuations of the spherical Sherrington-Kirkpatrick model

The spherical Sherrington-Kirkpatrick (SSK) model is one of the simplest spin glass models that arises naturally in spherical integrals and statistical applications. The SSK is defined by a Gibbs measure on a sphere that involves a random symmetric matrix. When the temperature is zero, the free energy of the SSK is equal to the largest eigenvalue of the random matrix. We will discuss how finite temperature cases are also related to random matrix theory. We will also consider the geometry of the Gibbs measure in the presence of an external field.