Isoperimetry and heat kernel decay on percolation clusters
Mathieu, Pierre ; Remy, Elisabeth
Ann. Probab., Tome 32 (2004) no. 1A, p. 100-128 / Harvested from Project Euclid
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We prove that the heat kernel on the infinite Bernoulli percolation cluster in $\Z^d$ almost surely decays faster than $t^{-d/2}$. We also derive estimates on the mixing time for the random walk confined to a finite box. Our approach is based on local isoperimetric inequalities. Some of the results of this paper were previously announced in the note of Mathieu and Remy [C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 927--931].
Publié le : 2004-01-14
Classification:  Percolation,  isoperimetry,  spectral gap,  heat kernel decay,  60J10,  60D05 
@article{1078415830,
     author = {Mathieu, Pierre and Remy, Elisabeth},
     title = {Isoperimetry and heat kernel decay on percolation clusters},
     journal = {Ann. Probab.},
     volume = {32},
     number = {1A},
     year = {2004},
     pages = { 100-128},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1078415830}
}

Mathieu, Pierre; Remy, Elisabeth. Isoperimetry and heat kernel decay on percolation clusters. Ann. Probab., Tome 32 (2004) no. 1A, pp.  100-128. http://gdmltest.u-ga.fr/item/1078415830/