We provide a new exponential concentration inequality for first passage percolation valid for a wide class of edge times distributions. This improves and extends a result by Benjamini, Kalai and Schramm (Ann. Probab. 31 (2003)) which gave a variance bound for Bernoulli edge times. Our approach is based on some functional inequalities extending the work of Rossignol (Ann. Probab. 35 (2006)), Falik and Samorodnitsky (Combin. Probab. Comput. 16 (2007)).
Publié le : 2008-06-15
Classification:
Modified Poincaré inequality,
Concentration inequality,
Hypercontractivity,
First passage percolation,
60E15,
60K35
@article{1211819424,
author = {Bena\"\i m, Michel and Rossignol, Rapha\"el},
title = {Exponential concentration for first passage percolation through modified Poincar\'e inequalities},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {44},
number = {2},
year = {2008},
pages = { 544-573},
language = {en},
url = {http://dml.mathdoc.fr/item/1211819424}
}
Benaïm, Michel; Rossignol, Raphaël. Exponential concentration for first passage percolation through modified Poincaré inequalities. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp. 544-573. http://gdmltest.u-ga.fr/item/1211819424/