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Bounds for the annealed return probability on large finite percolation graphs


 
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1. Title Title of document Bounds for the annealed return probability on large finite percolation graphs
 
2. Creator Author's name, affiliation, country Florian Sobieczky; University of Denver; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Random walks; Annealed Return Probability; Critical Invariant Percolation; Anomalous Diffusion; Integrated Density of States; Number of open clusters per vertex
 
3. Subject Subject classification 47B80; 05C81; 60K35; 60J27
 
4. Description Abstract Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation and the associated heavy-tailed cluster size distributions.  The upper bound relies on the fact that cartesian products of finite graphs with cycles of a certain minimal size are Hamiltonian. For critical Bernoulli bond percolation on the homogeneous tree this bound is sharp. The asymptotic type of the expected return probability for large times $t$ in this case is of order $t^{-3/4}$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) FWF, Project P18703; University of Jena; University of Colorado at Boulder
 
7. Date (YYYY-MM-DD) 2012-09-21
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2329
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-2329
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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