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Random Walk Attracted by Percolation Clusters


 
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1. Title Title of document Random Walk Attracted by Percolation Clusters
 
2. Creator Author's name, affiliation, country Serguei Popov; Universidade de São Paulo, Brasil
 
2. Creator Author's name, affiliation, country Marina Vachkovskaia; Universidade de Campinas, Brasil
 
3. Subject Discipline(s)
 
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4. Description Abstract 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 $\beta$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2005-12-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1167
 
10. Identifier Digital Object Identifier 10.1214/ECP.v10-1167
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 10
 
12. Language English=en
 
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