Download this PDF file Fullscreen Fullscreen Off
References
- L. Addario-Berry, A. Sarkar. The simple random walk on a random Voronoi tiling. Preprint.
- M.T. Barlow, R.F. Bass, T. Kumagai. Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps. Math. Z. 261 (2009), 297-320. Math. Review 2009m:60111
- N. Berger. Transience, recurrence and critical behavior for long-range percolation. Commun. Math. Phys. 226 (2002), 531-558. Math. Review 2003a:82034
- J. Ben Hough, M. Krishnapur, Y. Peres, B.Virág. Determinantal processes and independence. Probability Surveys. 3 (2006), 206-229. Math. Review 2006m:60068
- I. Benjamini, R. Pemantle, Y. Peres. Unpredictable paths and percolation. Ann. Probab. 26 (1998), 1198-1211. Math. Review 99g:60183
- P. Caputo, A. Faggionato. Isoperimetric inequalities and mixing time for a random walk on a random point process. Ann. Appl. Probab. 17 (2007), 1707-1744. Math. Review 2008m:60204
- P. Caputo, A. Faggionato. Diffusivity in one-dimensional generalized Mott variable-range hopping models. Ann. Appl. Probab. 19 (2009), 1459-1494. Math. Review number not available.
- D.J. Delay, D. Vere-Jones. An introduction to the theory of point processes. Vol. I, Second edition. Springer-Verlag, 2003.
- P.G. Doyle, J.L. Snell. Random walks and electric networks. The Carus mathematical monographs 22, Mathematical Association of America, Washington, 1984. Math. Review 89a:94023
- R.A. Doney. One-sided local large deviation and renewal theorems in the case of infinite mean. Probab. Theory Rel. Fields 107 (1997), 451-465. Math. Review 98e:60040
- A. Faggionato, P. Mathieu. Mott law as upper bound for a random walk in a random environment. Comm. Math. Phys. 281 (2008), 263-286. Math. Review 2009b:60309
- A. Faggionato, H. Schulz--Baldes, D. Spehner. Mott law as lower bound for a random walk in a random environment. Comm. Math. Phys. 263 (2006), 21-64. Math. Review 2007c:82034
- A. Gaudillière. Condenser physics applied to Markov chains - A brief introduction to potential theory. Lecture notes.
- H.-O. Georgii, T. Küneth. Stochastic comparison of point random fields. J. Appl. Probab. 34 (1997), 868-881. Math. Review 99c:60101
- G. Grimmett. Percolation. Second edition. Springer, Grundlehren 321, Berlin, 1999. Math. Review 2001a:60114
- G. Grimmett, H. Kesten, Y. Zhang. Random walk on the infinite cluster of the percolation model. Probab. Theory Rel. Fields 96, no. 1 (1993), 33-44. Math. Review 94i:60078
- T. Kumagai, J. Misumi. Heat kernel estimates for strongly recurrent random walk on random media. J. Theoret. Probab. 21 (2008), 910-935. Math. Review 2009g:35101
- J. Kurkijärvi. Hopping conductivity in one dimension. Phys. Rev. B, 8, no. 2 (1973), 922--924.
- T. Lyons. A simple criterion for transience of a reversible Markov chain. Ann. Probab. 11, no. 2 (1983), 393-402. Math. Review 84e:60102
- R. Lyons, Y. Peres. Probability on Trees and Networks. Book in progress.
- R. Lyons, J. Steif. Stationary determinantal processes: Phase multiplicity, Bernoullicity, Entropy, and Domination. Duke Math. Journal 120 (2003), 515-575. Math. Review 2004k:60100
- J. Misumi. Estimates on the effective resistance in a long-range percolation on Z^d. Kyoto U. Math. Journal 48, no.2 (2008), 389-400. Math. Review 2009d:60332
- A. Pisztora. Surface order large deviations for Ising, Potts and percolation models. Probab. Theory Rel. Fields 104 (1996), 427-466. Math. Review 97d:82016
- A. Soshnikov. Determinantal random point fields. Russian Mathematical Surveys 55 (2000), 923-975. Math. Review 2002f:60097
- F. Spitzer. Principles of random walk . Second edition, Graduate Texts in Mathematics, Vol. 34. Springer-Verlag, 1976. Math. Review 52#9383

This work is licensed under a Creative Commons Attribution 3.0 License.