# In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusReflecting Random Walks in Curvilinear Wedges

In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius: Reflecting Random Walks in... [We study a random walk (Markov chain) in an unbounded planar domain bounded by two curves of the form x2=a+x1β+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x_2 = a^+ x_1^{\beta ^+}$$ \end{document} and x2=−a−x1β−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x_2 = -a^- x_1^{\beta ^-}$$ \end{document}, 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.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# In and Out of Equilibrium 3: Celebrating Vladas SidoraviciusReflecting Random Walks in Curvilinear Wedges

Part of the Progress in Probability Book Series (volume 77)
Editors: Vares, Maria Eulália; Fernández, Roberto; Fontes, Luiz Renato; Newman, Charles M.
38 pages

# References (39)

Publisher
Springer International Publishing
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
ISBN
978-3-030-60753-1
Pages
637 –675
DOI
10.1007/978-3-030-60754-8_26
Publisher site
See Chapter on Publisher Site

### Abstract

[We study a random walk (Markov chain) in an unbounded planar domain bounded by two curves of the form x2=a+x1β+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x_2 = a^+ x_1^{\beta ^+}$$ \end{document} and x2=−a−x1β−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$x_2 = -a^- x_1^{\beta ^-}$$ \end{document}, 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.]

Published: Nov 4, 2020

Keywords: Reflected random walk; Generalized parabolic domain; Recurrence; Transience; Passage-time moments; Normal reflection; Oblique reflection; 60J05 (Primary); 60J10; 60G50 (Secondary)