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2005 Random Walk Attracted by Percolation Clusters
Serguei Popov, Marina Vachkovskaia
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Electron. Commun. Probab. 10: 263-272 (2005). DOI: 10.1214/ECP.v10-1167


Starting with a percolation model in $\mathbb{Z}^d$ in the subcritical regime, we consider a random walk described as follows: the probability of transition from $x$ to $y$ is proportional to some function $f$ of the size of the cluster of $y$. This function is supposed to be increasing, so that the random walk is attracted by bigger clusters. For $f(t)=e^{\beta t}$ we prove that there is a phase transition in $\beta$, i.e., the random walk is subdiffusive for large $\beta$ and is diffusive for small $\beta$.


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Serguei Popov. Marina Vachkovskaia. "Random Walk Attracted by Percolation Clusters." Electron. Commun. Probab. 10 263 - 272, 2005.


Accepted: 21 December 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1112.60089
MathSciNet: MR2198601
Digital Object Identifier: 10.1214/ECP.v10-1167

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