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Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates (2024)
Journal Article
Menshikov, M. V., Popov, S., & Wade, A. R. (in press). Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates. Mathematical Sciences,

We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppre... Read More about Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates.

Iterated-logarithm laws for convex hulls of random walks with drift (2024)
Journal Article
Cygan, W., Sandrić, N., Šebek, S., & Wade, A. R. (2024). Iterated-logarithm laws for convex hulls of random walks with drift. Transactions of the American Mathematical Society, 377(9), 6695-6724

We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero drift. Analogous results in the case of zero drift, where the scaling is... Read More about Iterated-logarithm laws for convex hulls of random walks with drift.

Superdiffusive planar random walks with polynomial space–time drifts (2024)
Journal Article
da Costa, C., Menshikov, M., Shcherbakov, V., & Wade, A. (2024). Superdiffusive planar random walks with polynomial space–time drifts. Stochastic Processes and their Applications, 176, Article 104420. https://doi.org/10.1016/j.spa.2024.104420

We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates... Read More about Superdiffusive planar random walks with polynomial space–time drifts.