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

   
@article{EJP1826,
	author = {Christophe Gallesco and Serguei Popov},
	title = {Random walks with unbounded jumps among random conductances I: Uniform quenched CLT},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {ergodic environment; unbounded jumps; hitting probabilities; exit distribution},
	abstract = {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 $O(\sqrt{n})$ around the origin.},
	pages = {no. 85, 1-22},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1826},    
        url = {http://ejp.ejpecp.org/article/view/1826}}