Outputs (8)

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.

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.

A radial invariance principle for non-homogeneous random walks (2018)
Journal Article
Georgiou, N., Mijatović, A., & Wade, A. R. (2018). A radial invariance principle for non-homogeneous random walks. Electronic Communications in Probability, 23, Article 56. https://doi.org/10.1214/18-ecp159

Consider non-homogeneous zero-drift random walks in Rd, d≥2, with the asymptotic increment covariance matrix σ2(u) satisfying u⊤σ2(u)u=U and trσ2(u)=V in all in directions u∈Sd−1 for some positive constants U

Anomalous recurrence properties of many-dimensional zero-drift random walks (2016)
Journal Article
Georgiou, N., Menshikov, M. V., Mijatovic, A., & Wade, A. R. (2016). Anomalous recurrence properties of many-dimensional zero-drift random walks. Advances in Applied Probability, 48(Issue A), 99-118. https://doi.org/10.1017/apr.2016.44

Famously, a d-dimensional, spatially homogeneous random walk whose increments are nondegenerate, have finite second moments, and have zero mean is recurrent if d∈{1,2}, but transient if d≥3. Once spatial homogeneity is relaxed, this is no longer true... Read More about Anomalous recurrence properties of many-dimensional zero-drift random walks.

New Constructions and Bounds for Winkler's Hat Game (2015)
Journal Article
Gadouleau, M., & Georgiou, N. (2015). New Constructions and Bounds for Winkler's Hat Game. SIAM Journal on Discrete Mathematics, 29(2), 823-834. https://doi.org/10.1137/130944680

Hat problems have recently become a popular topic in combinatorics and discrete mathematics. These have been shown to be strongly related to coding theory, network coding, and auctions. We consider the following version of the hat game, introduced by... Read More about New Constructions and Bounds for Winkler's Hat Game.

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.

The simple harmonic urn (2011)
Journal Article
Crane, E., Georgiou, N., Volkov, S., Wade, A. R., & Waters, R. J. (2011). The simple harmonic urn. Annals of Probability, 39(6), 2119-2177. https://doi.org/10.1214/10-aop605

We study a generalized Pólya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, t... Read More about The simple harmonic urn.