We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Reflecting random walks in curvilinear wedges.

Menshikov, Mikhail V. and Mijatović, Aleksandar and Wade, Andrew R. 'Reflecting random walks in curvilinear wedges.', in In and out of equilibrium 3: celebrating Vladas Sidoarvicius. , pp. 637-675. Progress in probability., 77


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.

Item Type:Book chapter
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher 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:
Date accepted:22 June 2020
Date deposited:08 December 2020
Date of first online publication:2021
Date first made open access:02 July 2022

Save or Share this output

Look up in GoogleScholar