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- W2954621925 abstract "We consider the limiting process that arises at the hard edge of Muttalib--Borodin ensembles. This point process depends on $theta > 0$ and has a kernel built out of Wright's generalized Bessel functions. In a recent paper, Claeys, Girotti and Stivigny have established first and second order asymptotics for large gap probabilities in these ensembles. These asymptotics take the form begin{equation*} mathbb{P}(mbox{gap on } [0,s]) = C exp left( -a s^{2rho} + b s^{rho} + c ln s right) (1 + o(1)) qquad mbox{as }s to + infty, end{equation*} where the constants $rho$, $a$, and $b$ have been derived explicitly via a differential identity in $s$ and the analysis of a Riemann--Hilbert problem. Their method can be used to evaluate $c$ (with more efforts), but does not allow for the evaluation of $C$. In this work, we obtain expressions for the constants $c$ and $C$ by employing a differential identity in $theta$. When $theta$ is rational, we find that $C$ can be expressed in terms of Barnes' $G$-function. We also show that the asymptotic formula can be extended to all orders in $s$." @default.
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- W2954621925 date "2019-06-28" @default.
- W2954621925 modified "2023-10-01" @default.
- W2954621925 title "Higher order large gap asymptotics at the hard edge for Muttalib--Borodin ensembles" @default.
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