CS10: Dynamics of stochastic particle systems
date: 7/17/2025, time: 16:00-17:30, room: ICS 13
Organizer: Sergio Andraus (Japan International University)
Chair: Sergio Andraus (Japan International University)
Optimal Bounds For The Dunkl Kernel In The Dihedral Case
Bartosz Trojan (PWr)
In this talk, we present how we have established sharp upper and lower estimates of the Dunkl kernel in the case of dihedral groups. Our strategy consists in using the differential-difference equations satisfied by the kernel, and in constructing appropriate barrier functions. The talk is based on the joint work with Jean-Philippe Anker.
Collisions in one-dimensional particle systems
Nicole Hufnagel (Heinrich Heine University Düsseldorf)
In this joint work we consider a general one-dimensional particle
system. These processes are mainly characterized by multiplicity
parameters controlling the strength of the particles’ interaction. It is
well-known that collisions between particles never take place when all
of these multiplicities are large, but occur almost surely otherwise.
It was recently shown by the authors that the collision times in the
special case of multivariate Bessel processes of rational type is a
piecewise-linear function of the minimum of its multiplicities, but is
independent of the dimension of the process’s domain. This implies that
the Hausdorff dimension does not depend on the particle number.
In this talk, we present an approach to extend this result to a general
particle system.