Professor Mikhail Menshikov mikhail.menshikov@durham.ac.uk
Professor
Reflecting random walks in curvilinear wedges
Menshikov, Mikhail V.; Mijatović, Aleksandar; Wade, Andrew R.
Authors
Aleksandar Mijatović
Professor Andrew Wade andrew.wade@durham.ac.uk
Professor
Contributors
M.E. Vares
Editor
R. Fernández
Editor
L.R. Fontes
Editor
C.M. Newman
Editor
Abstract
We study a random walk (Markov chain) in an unbounded planar domain bounded by two curves of the form x2=a+xβ+1 and x2=−a−xβ−1 , with x1 ≥ 0. In the interior of the domain, the random walk has zero drift and a given increment covariance matrix. From the vicinity of the upper and lower sections of the boundary, the walk drifts back into the interior at a given angle α+ or α− to the relevant inwards-pointing normal vector. Here we focus on the case where α+ and α− are equal but opposite, which includes the case of normal reflection. For 0 ≤ β+, β− < 1, we identify the phase transition between recurrence and transience, depending on the model parameters, and quantify recurrence via moments of passage times.
Citation
Menshikov, M. V., Mijatović, A., & Wade, A. R. (2021). Reflecting random walks in curvilinear wedges. In M. Vares, R. Fernández, L. Fontes, & C. Newman (Eds.), In and out of equilibrium 3: celebrating Vladas Sidoarvicius (637-675). Springer Verlag. https://doi.org/10.1007/978-3-030-60754-8_26
Publication Date | 2021 |
---|---|
Deposit Date | Jun 19, 2020 |
Publicly Available Date | Jul 2, 2022 |
Publisher | Springer Verlag |
Pages | 637-675 |
Series Title | Progress in probability |
Series Number | 77 |
Book Title | In and out of equilibrium 3: celebrating Vladas Sidoarvicius. |
ISBN | 9783030607531 |
DOI | https://doi.org/10.1007/978-3-030-60754-8_26 |
Public URL | https://durham-repository.worktribe.com/output/1657018 |
Publisher URL | https://www.springer.com/gp/book/9783030607531 |
Related Public URLs | https://arxiv.org/abs/2001.06685 |
Contract Date | Jun 22, 2020 |
Files
Accepted Book Chapter
(430 Kb)
PDF
Copyright Statement
This a post-peer-review, pre-copyedit version of a chapter published in In and out of equilibrium 3: celebrating Vladas Sidoarvicius. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-60754-8_26
You might also like
Dynamics of Finite Inhomogeneous Particle Systems with Exclusion Interaction
(2023)
Journal Article
Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
(2023)
Journal Article
Stochastic billiards with Markovian reflections in generalized parabolic domains
(2023)
Journal Article
Random walks avoiding their convex hull with a finite memory
(2019)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search