Exponential concentration for first passage percolation through modified Poincare inequalities - Benaim, Michel; Rossignol, Raphael (My University, 2008)
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)).
Keywords: modified Poincare inequality; concentration inequality; hypercontractivity; first passage percolation; FLUCTUATIONS