Résumé

Beta ensemble is one of the fundamental object in random matrix theory, describing the Gibbs measure of 1dim $N$ particles under the log potential at inverse temperature $\beta$. High temperature limit refers to consider $\beta \to 0$ limit such that $N \beta = c$. By changing $c$, it is expected to interpolate between the classical ($c=0$) and free ($c=\infty$) probability theory. In this talk, I will review them and mention our recent results on Markov Klein transform and finite free convolutions. This is a joint work with Khanh Duy Trinh, Dung Hoang Trinh, and Ziteng Wang

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