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We provide an introduction to recent results on the large N behavior of beta-ensembles, also known as log-gases. In the first part, we focus on the rigidity property of the spectrum which provides fine estimates on the fluctuations of eigenvalues and explain how this relate to universality. In the second part, we explain how to prove the CLT for linear statistics using loop equations and mention the connection to log-correlated fields and Gaussian multiplicative chaos.Updated on Oct 22, 2021 08:18 AM PDT
Updated on Aug 24, 2021 11:21 AM PDT
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