UVictoria Probability and Dynamics Seminar: Qiang Wu

Spin glasses are disordered statistical physics system with both ferromagnetic and anti-ferromagnetic spin interactions. The Gibbs measure belongs to the exponential family with parameters, such as inverse temperature $\beta>0$ and external field $h\in R$. Given a sample from the Gibbs measure of a spin glass model, we study the problem of estimating system parameters. In 2007, Chatterjee first proved that under reasonable conditions, for spin glass models with $h=0$, the maximum pseudo-likelihood estimator for $\beta$ is $\sqrt{N}$-consistent. However, the approach has been restricted to the single parameter estimation setting. The joint estimation of $(\beta,h)$ for spin glasses has remained open. In this talk, I will present a joint work with Wei-Kuo Chen, Arnab Sen, which shows that under some easily verifiable conditions, the bi-variate maximum pseudo-likelihood estimator is indeed jointly $\sqrt{N}$-consistent for a large collection of spin glasses, including the Sherrington-Kirkpatrick model and its diluted variants.