Fluctuations of linear eigenvalue statistics of $\beta$ matrix models in   the multi-cut regime
  We study the asymptotic expansion in $n$ for the partition function of $\beta$ matrix models with real analytic potentials in the multi-cut regime up to the $O(n^{-1})$ terms. As a result, we find the limit of the generating functional of linear eigenvalue statistics and the expressions for the expectation and the variance of linear eigenvalue statistics, which in the general case contain the quasi periodic in $n$ terms. 
Mariya Shcherbina
math-ph math.MP