For high-temperature 1D log gases, the rescaled largest particle obeys a large deviation principle with the iid rate function x^d - 1, and tridiagonal matrices with Gaussian tails obey the analogous principle with rate x^2 - 1.
Poisson Statistics for Coulomb Gases at Intermediate Temperature Regimes
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abstract
We consider the microscopic statistics of a Coulomb gas in $\mathbb{R}^2$ at intermediate temperatures. In particular, we show that the microscopic point process associated to the Coulomb gas converges to a homogeneous Poisson point process at intermediate temperature regimes $\beta N \rightarrow \infty$ and $\beta \sqrt{N} \log N \rightarrow 0$, extending previous results. Our approach relies on a novel quantitative asymptotic description of correlation functions, which is of its own interest.
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Large deviations at the edge for 1D gases and tridiagonal random matrices at high temperature
For high-temperature 1D log gases, the rescaled largest particle obeys a large deviation principle with the iid rate function x^d - 1, and tridiagonal matrices with Gaussian tails obey the analogous principle with rate x^2 - 1.