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math-ph2018★ 20 cited
Painlevé III and the Hankel Determinant Generated by a Singularly Perturbed Gaussian Weight
Chao Min, Shulin Lyu, Yang Chen
In this paper, we study the Hankel determinant generated by a singularly perturbed Gaussian weight $$ w(x,t)=\mathrm{e}^{-x^{2}-\frac{t}{x^{2}}},\;\;x\in(-\infty, \infty),\;\;t>0.…
math-ph2018★ 26 cited
Asymptotic Gap Probability Distributions of the Gaussian Unitary Ensembles and Jacobi Unitary Ensembles
Shulin Lyu, Yang Chen, Engui Fan
In this paper, we address a class of problems in unitary ensembles. Specifically, we study the probability that a gap symmetric about 0, i.e. is found in the Gaussian unit…