Asymptotics of a two-dimensional sticky random walk

Details Asymptotics of a two-dimensional sticky random walk Asymptotics of a two-dimensional sticky random walk

2004-05-24

arxiv.org/abs/math/0405451v1

Mathematics

Probability

9 pages

Scientific paper

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 $\Delta$ with respect
to the number of steps performed by the chain.

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