Return to Colloquia & Seminar listing
Stochastic Billiards with Markovian reflection in generalized parabolic domains
Probability| Speaker: | Conrado Da-Costa, Durham University |
| Related Webpage: | https://www.maths.dur.ac.uk/users/conrado.da-costa/ |
| Location: | Zoom |
| Start time: | Wed, Apr 27 2022, 1:10PM |
In this talk, we consider a particle moving linearly inside generalized parabolic domain with Markovian reflection at the boundary.
Our goal is to determine, with respect to the reflection law, when the process is recurrent or transient.
The central idea, which applies a class of non-homogeneous random walks, is to find a Lyapunov function for the properly rescaled version of the problem.
Next, we employ supermartingale methods to identify, given the reflection kernel, a phase transition, from recurrent to transient, as we change a single geometric parameter of the region for these stochastic billiards.
The solution of this problem is done via a translation to a broad class of almost Markovian models, the half-strip models, and makes use of some tools from functional analysis. This is a joint work with Mikhail Menshikov and Andrew Wade.
Zoom L.: https://ucdavis.zoom.us/j/99375733459