Dr Conrado Da Costa conrado.da-costa@durham.ac.uk
Assistant Professor
Stochastic billiards with Markovian reflections in generalized parabolic domains
da Costa, Conrado; Menshikov, Mikhail V.; Wade, Andrew R.
Authors
Professor Mikhail Menshikov mikhail.menshikov@durham.ac.uk
Professor
Professor Andrew Wade andrew.wade@durham.ac.uk
Professor
Abstract
We study recurrence and transience for a particle that moves at constant velocity in the interior of an unbounded planar domain, with random reflections at the boundary governed by a Markov kernel producing outgoing angles from incoming angles. Our domains have a single unbounded direction and sub-linear growth. We characterize recurrence in terms of the reflection kernel and growth rate of the domain. The results are obtained by transforming the stochastic billiards model to a Markov chain on a half-strip R+ × S where S is a compact set. We develop the recurrence classification for such processes in the near-critical regime in which drifts of the R+ component are of generalized Lamperti type, and the S component is asymptotically Markov; this extends earlier work that dealt with finite S
Citation
da Costa, C., Menshikov, M. V., & Wade, A. R. (2023). Stochastic billiards with Markovian reflections in generalized parabolic domains. Annals of Applied Probability, 33(6B), 5459-5496. https://doi.org/10.1214/23-AAP1952
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 11, 2023 |
Online Publication Date | Dec 13, 2023 |
Publication Date | 2023-12 |
Deposit Date | Aug 9, 2021 |
Publicly Available Date | Dec 13, 2023 |
Journal | Annals of Applied Probability |
Print ISSN | 1050-5164 |
Publisher | Institute of Mathematical Statistics |
Peer Reviewed | Peer Reviewed |
Volume | 33 |
Issue | 6B |
Pages | 5459-5496 |
DOI | https://doi.org/10.1214/23-AAP1952 |
Public URL | https://durham-repository.worktribe.com/output/1237971 |
Related Public URLs | https://doi.org/10.48550/arXiv.2107.13976 |
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