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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…
math.PR2023
Probabilistic models motivated by cooperative sequential adsorption
Vadim Shcherbakov
This survey concerns probabilistic models motivated by cooperative sequential adsorption (CSA) models. CSA models are widely used in physics and chemistry for modelling adsorption…