A modified Poincare inequality and its application to First Passage Percolation

2006/02/22 by Benaim, Michel, Rossignol, Raphael
#FOS: Mathematics #Primary: 60E15 #Probability (math.PR) #secondary: 60K35

paper · doi:10.48550/arxiv.math/0602496

Abstract

We extend a Gaussian functional inequality to a countable product of Gaussian measures. This inequality improves on the classical Poincare inequality for Gaussian measures. As an application, we prove that First Passage Percolation has sublinear variance when the edge times distribution belongs to a wide class of continuous distributions, including the exponential one. This extends a result by Benjamini, Kalai and Schramm, valid for positive Bernoulli edge times.

Related

• Exponential concentration for First Passage Percolation through modified Poincare inequalities
• Fluctuations in first-passage percolation
• Variance bounds for Gaussian first passage percolation
• Higher-order derivatives of first-passage percolation with respect to the environment
• Small ball probabilities for the passage time in planar first-passage percolation