The random conductance model with Cauchy tails

Barlow, Martin T.; Zheng, Xinghua

Ann. Appl. Probab., Tome 20 (2010) no. 1, p. 869-889 / Harvested from Project Euclid

Résumé

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 p_n²t^ω(0, y) in [Ann. Probab. (2009). To appear], Theorem 5.14, to a result which gives uniform convergence for p_n²t^ω(x, y) for all x, y in a ball.

Publié le : 2010-06-15
Classification: Random conductance model, heat kernel, invariance principle, 60K37, 60F17, 82C41

@article{1276867300,
     author = {Barlow, Martin T. and Zheng, Xinghua},
     title = {The random conductance model with Cauchy tails},
     journal = {Ann. Appl. Probab.},
     volume = {20},
     number = {1},
     year = {2010},
     pages = { 869-889},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1276867300}
}

Barlow, Martin T.; Zheng, Xinghua. The random conductance model with Cauchy tails. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp.  869-889. http://gdmltest.u-ga.fr/item/1276867300/