Skip to main content

Research Repository

Advanced Search

All Outputs (4)

Convex hulls of planar random walks with drift (2014)
Journal Article
Wade, A. R., & Xu, C. (2015). Convex hulls of planar random walks with drift. Proceedings of the American Mathematical Society, 143(1), 433-445. https://doi.org/10.1090/s0002-9939-2014-12239-8

Denote by Ln the length of the perimeter of the convex hull of n steps of a planar random walk whose increments have nite second moment and non-zero mean. Snyder and Steele showed that -1 Ln converges almost surely to a deterministic limit, and prove... Read More about Convex hulls of planar random walks with drift.

Rank deficiency in sparse random GF[2] matrices (2014)
Journal Article
Darling, R. W., Penrose, M. D., Wade, A. R., & Zabell, S. L. (2014). Rank deficiency in sparse random GF[2] matrices. Electronic Journal of Probability, 19, Article 83. https://doi.org/10.1214/ejp.v19-2458

Let M be a random m×n matrix with binary entries and i.i.d. rows. The weight (i.e., number of ones) of a row has a specified probability distribution, with the row chosen uniformly at random given its weight. Let N(n,m) denote the number of left null... Read More about Rank deficiency in sparse random GF[2] matrices.

Non-homogeneous random walks on a semi-infinite strip (2014)
Journal Article
Georgiou, N., & Wade, A. R. (2014). Non-homogeneous random walks on a semi-infinite strip. Stochastic Processes and their Applications, 124(10), 3179-3205. https://doi.org/10.1016/j.spa.2014.05.005

We study the asymptotic behaviour of Markov chains (Xn,ηn) on Z+×S, where Z+ is the non-negative integers and S is a finite set. Neither coordinate is assumed to be Markov. We assume a moments bound on the jumps of Xn, and that, roughly speaking, ηn... Read More about Non-homogeneous random walks on a semi-infinite strip.