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
Outputs (4)
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-ejp302We 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-aap1434Each 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.