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比利时vs摩洛哥足彩 ,
university of california san diego

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math 288 - probability & statistics

karl liechty

de paul university

tacnode processes, winding numbers, and painleve ii

abstract:

i will discuss a model of nonintersecting brownian bridges on the unit circle, which produces quite a few universal determinantal processes as scaling limits. i will focus on the tacnode process, in which two groups of particles meet at a single point in space-time before separating, and introduce a new version of the tacnode process in which a finite number of particles ``switch sides'' before the two groups separate. we call this new process the k-tacnode process, and it is defined by a kernel expressed in terms of a system of tau-functions for the painleve ii equation. technically, our model of nonintersecting brownian bridges on the unit circle is studied using a system of discrete orthogonal polynomials with a complex (non-hermitian) weight, so i'll also discuss some of the analytical obstacles to that analysis. \noindent this is joint work with dong wang and robert buckingham

host: tianyi zheng

march 15, 2018

10:00 am

ap&m 6402

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