Exponential concentration for first passage percolation through modified Poincaré inequalities
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)).