Section: New Results

DLR equations and rigidity for the Sine-beta process

The Sine-beta process is a universal object appearing in the study of large Hermitian random matrices and statistical systems in a logarithmic interaction, such as low dimensional Coulomb gases. However, the only description available yet relied on a rather complicated and non-physical system of coupled stochastic differential equations. In [21], D. Dereudre, A. Hardy, T. Leblé and M. Maïda obtain a statistical physic interpretation of the Sine-beta process as probability measure on infinite configurations of points described by means of the DLR formalism. This allows to obtain more information on the Sine-beta process: for instance, it is rigid, it is tolerant, and the number of particles in a compact box has gaussian fluctuations as the box becomes large.