Let $\lambda=(\lambda_1, \cdots, \lambda_n)$ be $\beta$-Jacobi ensembles with parameters $p_1, p_2, n$ and $\beta,$ with $\beta$ varying with $n.$ Set $\gamma=\lim\limits_{n\rightarrow\infty}\frac{n}{p_1}$ and $\sigma=\lim\limits_{n\rightarrow\infty}\frac{p_1}{p_2}.$ Suppose that $\lim\limits_{n\to\infty}\frac{\log n}{\beta n}=0$ and $0\le \sigma\gamma< 1.$ We offer the large deviation for $\frac{p_1+p_2}{p_1}\max\limits_{1\le i\le n}\lambda_{i}$ when $\gamma>0$ via the large deviation of the corresponding empirical measure and via a direct estimate, respectively, when $\gamma=0.$
Liangzhen LEI
,
Yutao MA
. LARGE DEVIATIONS FOR TOP EIGENVALUES OF ß -JACOBI ENSEMBLES AT SCALING TEMPERATURES∗[J]. Acta mathematica scientia, Series B, 2023
, 43(4)
: 1767
-1780
.
DOI: 10.1007/s10473-023-0418-7
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