Outputs (55)

Deposition, diffusion, and nucleation on an interval (2022)
Journal Article
Georgiou, N., & Wade, A. R. (2022). Deposition, diffusion, and nucleation on an interval. Annals of Applied Probability, 32(6), 4849-4892. https://doi.org/10.1214/22-aap1804

Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier... Read More about Deposition, diffusion, and nucleation on an interval.

Cutpoints of non-homogeneous random walks (2022)
Journal Article
Lo, C. H., Menshikov, M. V., & Wade, A. R. (2022). Cutpoints of non-homogeneous random walks. Alea (2006. Online), 19, 493-510. https://doi.org/10.30757/alea.v19-19

We give conditions under which near-critical stochastic processes on the half-line have infinitely many or finitely many cutpoints, generalizing existing results on nearest-neighbour random walks to adapted processes with bounded increments satisfyin... Read More about Cutpoints of non-homogeneous random walks.

Reflecting random walks in curvilinear wedges (2021)
Book Chapter
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

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... Read More about Reflecting random walks in curvilinear wedges.

Angular asymptotics for random walks (2021)
Book Chapter
López Hernández, A., & Wade, A. R. (2021). Angular asymptotics for random walks. In L. Chaumont, & A. E. Kyprianou (Eds.), A Lifetime of Excursions Through Random Walks and Lévy Processes (315-342). Springer Verlag. https://doi.org/10.1007/978-3-030-83309-1_17

We study the set of directions asymptotically explored by a spatially homogeneous random walk in d-dimensional Euclidean space. We survey some pertinent results of Kesten and Erickson, make some further observations, and present some examples. We als... Read More about Angular asymptotics for random walks.

Markov Chains (2020)
Journal Article
Wade, A. R. (online). Markov Chains

Random walks avoiding their convex hull with a finite memory (2019)
Journal Article
Comets, F., Menshikov, M. V., & Wade, A. R. (2020). Random walks avoiding their convex hull with a finite memory. Indagationes Mathematicae, 31(1), 117-146. https://doi.org/10.1016/j.indag.2019.11.002

Markov chains with heavy-tailed increments and asymptotically zero drift (2019)
Journal Article
Georgiou, N., Menshikov, M. V., Petritis, D., & Wade, A. R. (2019). Markov chains with heavy-tailed increments and asymptotically zero drift. Electronic Journal of Probability, 24, Article 62. https://doi.org/10.1214/19-ejp322

Invariance principle for non-homogeneous random walks (2019)
Journal Article
Georgiou, N., Mijatović, A., & Wade, A. R. (2019). Invariance principle for non-homogeneous random walks. Electronic Journal of Probability, 24, https://doi.org/10.1214/19-ejp302

We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in Rd, which may be recurrent in any dimension. The limit X is an elliptic martingale diffusion, which may be point-recurrent at the origin for any d 2.... Read More about Invariance principle for non-homogeneous random walks.

The critical greedy server on the integers is recurrent (2019)
Journal Article
Cruise, J. R., & Wade, A. R. (2019). The critical greedy server on the integers is recurrent. Annals of Applied Probability, 29(2), 1233-1261. https://doi.org/10.1214/18-aap1434

Each site of Z hosts a queue with arrival rate λ. A single server, starting at the origin, serves its current queue at rate μ until that queue is empty, and then moves to the longest neighbouring queue. In the critical case λ=μ, we show that the serv... Read More about The critical greedy server on the integers is recurrent.

The convex hull of a planar random walk: perimeter, diameter, and shape (2018)
Journal Article
McRedmond, J., & Wade, A. R. (2018). The convex hull of a planar random walk: perimeter, diameter, and shape. Electronic Journal of Probability, 23, Article 131. https://doi.org/10.1214/18-ejp257

We study the convex hull of the first n steps of a planar random walk, and present large-n asymptotic results on its perimeter length Ln, diameter Dn, and shape. In the case where the walk has a non-zero mean drift, we show that Ln=Dn ! 2 a.s., and g... Read More about The convex hull of a planar random walk: perimeter, diameter, and shape.