The Annals of Applied Probability

The random conductance model with Cauchy tails

Martin T. Barlow and Xinghua Zheng

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We consider a random walk in an i.i.d. Cauchy-tailed conductances environment. We obtain a quenched functional CLT for the suitably rescaled random walk, and, as a key step in the arguments, we improve the local limit theorem for pn2tω(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for pn2tω(x, y) for all x, y in a ball.

Article information

Ann. Appl. Probab., Volume 20, Number 3 (2010), 869-889.

First available in Project Euclid: 18 June 2010

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Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60F17: Functional limit theorems; invariance principles 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Random conductance model heat kernel invariance principle


Barlow, Martin T.; Zheng, Xinghua. The random conductance model with Cauchy tails. Ann. Appl. Probab. 20 (2010), no. 3, 869--889. doi:10.1214/09-AAP638.

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