Asymptotics of a two-dimensional sticky random walk

Jean Bérard

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Asymptotics of a two-dimensional sticky random walk

Jean Bérard

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Abstract

We study the asymptotic behavior of a Markov chain on $\mathbb{Z}^2$ that corresponds to the two-dimensional marginals of a reinforcement process on $\mathbb{Z}^{\mathbb{N}}$. Three distinct asymptotic regimes are identified, depending on the scaling of the reinforcement parameter $Δ$ with respect to the number of steps performed by the chain.

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Jean Bérard. 2004-05-24. Asymptotics of a two-dimensional sticky random walk. https://arxiv.org/abs/math/0405451

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