We use tridiagonal models to study the limiting behavior of β-Laguerre and β-Jacobi ensembles, focusing on the limiting behavior of the extremal eigenvalues and the central limit theorem for the two ensembles. For the central limit theorem of β-Laguerre ensembles, we follow the idea in [1] while giving a modified version for the generalized case. Then we use the total variation distance between the two sorts of ensembles to obtain the limiting behavior of β-Jacobi ensembles.
Naqi HUANG
,
Yutao MA
. LIMIT THEOREMS FOR β-LAGUERRE AND β-JACOBI ENSEMBLES[J]. Acta mathematica scientia, Series B, 2022
, 42(5)
: 2025
-2039
.
DOI: 10.1007/s10473-022-0517-x
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