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math.PR2025
A diffusion limit for Markov chains with log-linear interaction on a graph
Anatolii Puhalskii, Vadim Shcherbakov
In this paper we establish a diffusion limit for a multivariate continuous time Markov chain whose components are indexed by vertices of a finite graph. The components take values…
math.PR2024
Superdiffusive planar random walks with polynomial space-time drifts
Conrado da Costa, Mikhail Menshikov, Vadim Shcherbakov +1
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…