Universality of the conditional measure of the Bessel point process

by Leslie Molag (KU Leuven)

Location: 200B.02.18, Leuven
Time: Thursday November 22, 2018 at 14:00

The Sine, the Bessel and the Airy process are examples of Rigid point processes, whose conditional measures are almost surely an orthogonal polynomial ensemble. This is a relatively recent result by Alexander Bufetov.

In a more recent article Arno Kuijlaars and Erwin Miña-Díaz considered the Sine process, conditioned to an interval $I=[-R,R]$.

They proved that the conditional measure will converge back to the Sine process as $R\to\infty$.

In this talk we consider the Bessel process, which we condition to an interval $I=[0,R]$.

Indeed we show that the equivalent result holds for the Bessel process, the conditional measure will converge back to the Bessel process as $R\to \infty$.

We will make use of Riemann-Hilbert techniques and techniques from the recent article by Arno Kuijlaars and Erwin Miña-Díaz.

This is joint work with Marco Stevens.