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math-ph2025
Asymptotic expansion of the hard-to-soft edge transition
Luming Yao, Lun Zhang
By showing that the symmetrically transformed Bessel kernel admits a full asymptotic expansion for large parameter, we establish a hard-to-soft edge transition expansion. This reso…
math-ph2025
Asymptotics for the noncommutative Painlevé II equation
Junwen Liu, Luming Yao, Lun Zhang
In this paper, we are concerned with the following noncommutative Painlevé II equation \begin{equation*} \mathbf{D}^2 β_1 = 4\mathbf{s} β_1 +4 β_1 \mathbf{s} +8 β_1^3, \end{eq…
math-ph2025
The multiplicative constant in asymptotics of higher-order analogues of the Tracy-Widom distribution
Dan Dai, Wen-Gao Long, Shuai-Xia Xu +2
In this paper, we are concerned with higher-order analogues of the Tracy-Widom distribution, which describe the eigenvalue distributions in unitary random matrix models near critic…