A modified Poincare inequality and its application to First Passage Percolation

Details A modified Poincare inequality and its application to First Passage Percolation A modified Poincare inequality and its application to First Passage Percolation

2006-02-22

arxiv.org/abs/math/0602496v2

Mathematics

Probability

After having completed a first version of this paper, we were informed that our main inequality, which we claimed to be new, w

Scientific paper

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.

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