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SUMMARY:Large gap asymptotics at the hard edge for Muttalib-Borodin ensemb
 les - Jonatan Lenells (KTH - Royal Institute of Technology )
DTSTART:20190909T130000Z
DTEND:20190909T140000Z
UID:TALK129253@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:I will present joint work with Christophe Charlier and Julian 
 Mauersberger. <br> We consider the limiting process that arises at the har
 d edge of Muttalib-Borodin ensembles. This point process depends on $\\the
 ta &gt\; 0$ and has a kernel built out of Wright&#39\;s generalized Bessel
  functions. In a recent paper\, Claeys\, Girotti and Stivigny have establi
 shed first and second order asymptotics for large gap probabilities in the
 se ensembles. These asymptotics take the form<br> \\begin{equation*}<br> \
 \mathbb{P}(\\mbox{gap on } [0\,s]) = C \\exp \\left( -a s^{2\\rho} + b s^{
 \\rho} + c \\ln s \\right) (1 + o(1)) \\qquad  \\mbox{as }s \\to + \\infty
 \,<br> \\end{equation*}<br> where the constants $\\rho$\, $a$\, and $b$ ha
 ve been derived explicitly via a differential identity in $s$ and the anal
 ysis 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 t
 his work\, we obtain expressions for the constants $c$ and $C$ by employin
 g a differential identity in $\\theta$. When $\\theta$ is rational\, we fi
 nd that $C$ can be expressed in terms of Barnes&#39\; $G$-function. We als
 o show that the asymptotic formula can be extended to all orders in $s$.
LOCATION:Seminar Room 1\, Newton Institute
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