Large gap asymptotics at the hard edge for Muttalib-Borodin ensembles
Duration: 51 mins 4 secs
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| Description: |
Lenells, J
Monday 9th September 2019 - 14:00 to 15:00 |
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| Created: | 2019-09-09 15:14 |
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| Collection: | The complex analysis toolbox: new techniques and perspectives |
| Publisher: | Isaac Newton Institute |
| Copyright: | Lenells, J |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | I will present joint work with Christophe Charlier and Julian Mauersberger. We consider the limiting process that arises at the hard edge of Muttalib-Borodin ensembles. This point process depends on θ>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
P(gap on [0,s])=Cexp(−as2ρ+bsρ+clns)(1+o(1))as s→+∞, where the constants ρ, 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 θ. When θ 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. |
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