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Large deviation bounds for the volume of the largest cluster in 2D critical percolation


 
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1. Title Title of document Large deviation bounds for the volume of the largest cluster in 2D critical percolation
 
2. Creator Author's name, affiliation, country Demeter Kiss; Cambridge University and Tohoku University; United Kingdom
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) critical percolation; critical cluster; moment bounds
 
3. Subject Subject classification 82B43; 60K35
 
4. Description Abstract Let $M_n$ denote the number of sites in the largest cluster in site percolation on the triangular lattice inside a box side length $n$. We give lower and upper bounds on the probability that $M_n / \mathbb{E} M_n > x$ of the form $\exp(-Cx^{2/\alpha_1})$ for $x \geq 1$ and large $n$ with $\alpha_1 = 5/48$ and $C>0$. Our results extend to other two dimensional lattices and strengthen the previously known exponential upper bound derived by Borgs, Chayes, Kesten and Spencer [BCKS99]. Furthermore, under some general assumptions similar to those in [BCKS99], we derive a similar upper bound in dimensions $d > 2$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2014-05-31
 
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/3438
 
10. Identifier Digital Object Identifier 10.1214/ECP.v19-3438
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 19
 
12. Language English=en en
 
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