Random walks with unbounded jumps among random conductances I: uniform quenched CLT

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we prove a quenched uniform invariance principle for the random walk. This means that the rescaled trajectory of length n is (in a certain sense) close enough to the Brownian motion, uniformly with respect to the choice of the starting location in an interval of length O (root n) around the origin.We study a one-dimensional random walk among random conductances, with unbounded jumps. Assuming the ergodicity of the collection of conductances and a few other technical conditions (uniform ellipticity and polynomial bounds on the tails of the jumps) we1785122FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)FAPESP [2009/51139-3, 2009/52379-8]CNPq [300886/2008-0, 472431/2009-9]2009/51139–3; 2009/52379–8300886/2008–0; 472431/2009–