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- W4380480159 abstract "The Freud ensemble of random matrices is the unitary invariant ensemble corresponding to the weight $exp(-n |x|^{beta})$, $beta>0$, on the real line. We consider the local behaviour of eigenvalues near zero, which exhibits a transition in $beta$. If $betage 1$, it is described by the standard sine process. Below the critical value $beta=1$, it is described by a process depending on the value of $beta$, and we determine the first two terms of the large gap probability in it. This so called weak confinement range $0<beta<1$ corresponds to the Freud weight with the indeterminate moment problem. We also find the multiplicative constant in the asymptotic expansion of the Freud multiple integral for $betage 1$." @default.
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- W4380480159 date "2023-06-13" @default.
- W4380480159 modified "2023-09-26" @default.
- W4380480159 title "Weak and Strong Confinement in the Freud Random Matrix Ensemble and Gap Probabilities" @default.
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- W4380480159 doi "https://doi.org/10.1007/s00220-023-04749-y" @default.
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