Fluctuations of the free energy of spherical Sherrington-Kirkpatrick model
Spherical Sherrington-Kirkpatrick (SSK) model is an example of disordered systems. The model is described by a collection of probability measures (Gibbs measures) which themselves depend on external random variables (disorders). Due to this double randomness, the free energy is a random variable. The convergence of the free energy to a non-random value in the large dimensional limit is a famous result of Parisi and Talagrand. Here we consider the fluctuations of the free energy for the 2-spin SSK model. We use the random matrix theory and describe the law of the fluctuations at all temperature except for the critical temperature. This is a joint work with Ji Oon Li.