The Annals of Applied Probability

The random conductance model with Cauchy tails

Martin T. Barlow and Xinghua Zheng

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Abstract

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

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

Dates
First available in Project Euclid: 18 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1276867300

Digital Object Identifier
doi:10.1214/09-AAP638

Mathematical Reviews number (MathSciNet)
MR2680551

Zentralblatt MATH identifier
1196.60173

Subjects
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]

Keywords
Random conductance model heat kernel invariance principle

Citation

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. https://projecteuclid.org/euclid.aoap/1276867300


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References

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