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Title:聽Statistical mechanics of the circular Riesz gas.

Abstract:聽I will present results on the statistical mechanics of the one-dimensional Riesz gas, a particle system with repulsive power-law interactions. This model extends the log-gas, well-known in random matrix theory. Through the study of a partial differential equation, sometimes called the Helffer-Sj枚strand equation, we establish optimal fluctuations and correlations estimates. I will then explain how to prove the existence of a unique infinite volume limit for the Riesz gas.