Download this PDF file Fullscreen Fullscreen Off
References
- Borodin, A. N. Distribution of integral functionals of the Brownian motion process.(Russian) Problems of the theory of probability distribution, VII. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 119 (1982), 19--38, 237--238, 244. MR0666084 (84b:60103)
- Csáki, E.; Révész, P. Strong invariance for local times. Z. Wahrsch. Verw. Gebiete 62 (1983), no. 2, 263--278. MR0688990 (84e:60048)
- Dembo, Amir; Sznitman, Alain-Sol. A lower bound on the disconnection time of a discrete cylinder. In and out of equilibrium. 2, 211--227, Progr. Probab., 60, Birkhäuser, Basel, 2008. MR2477383
- Dembo, Amir and Zeitouni, Ofer. Large deviations techniques and applications. Springer, Berlin, 2nd edition, 1998.
- Eisenbaum, N. Un théorème de Ray-Knight lié au supremum des temps locaux browniens.(French) [A Ray-Knight theorem associated with the supremum of Brownian local times] Probab. Theory Related Fields 87 (1990), no. 1, 79--95. MR1076957 (92a:60168)
- Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes.Second edition.North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. xvi+555 pp. ISBN: 0-444-87378-3 MR1011252 (90m:60069)
- Kesten, Harry. Percolation theory for mathematicians.Progress in Probability and Statistics, 2. Birkhäuser, Boston, Mass., 1982. iv+423 pp. ISBN: 3-7643-3107-0 MR0692943 (84i:60145)
- Lawler, Gregory F. Intersections of random walks.Probability and its Applications. Birkhäuser Boston, Inc., Boston, MA, 1991. 219 pp. ISBN: 0-8176-3557-2 MR1117680 (92f:60122)
- Liggett, Thomas M. Interacting particle systems.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 276. Springer-Verlag, New York, 1985. xv+488 pp. ISBN: 0-387-96069-4 MR0776231 (86e:60089)
- Lindvall, Torgny. Lectures on the coupling method.Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. A Wiley-Interscience Publication.John Wiley & Sons, Inc., New York, 1992. xiv+257 pp. ISBN: 0-471-54025-0 MR1180522 (94c:60002)
- Sidoravicius, Vladas; Sznitman, Alain-Sol. Percolation for the vacant set of random interlacements. Comm. Pure Appl. Math. 62 (2009), no. 6, 831--858. MR2512613
- V. Sidoravicius and A.S. Sznitman. Connectivity bounds for the vacant set of random interlacements. Preprint, also available at: http://www.math.ethz.ch/u/sznitman/preprints.
- A.S. Sznitman. Vacant set of random interlacements and percolation. \newblock {\em Ann. Math., in press, also available at: http://www.math.ethz.ch/u/sznitman/preprints.
- A.S. Sznitman. Random walks on discrete cylinders and random interlacements. Probab. Theory Relat. Fields, 145:143--174, 2009.
- A.S. Sznitman. Upper bound on the disconnection time of discrete cylinders and random interlacements. Ann Probab., in press, also available at: http://www.math.ethz.ch/u/sznitman/preprints
- Teixeira, Augusto. On the uniqueness of the infinite cluster of the vacant set of random interlacements. Ann. Appl. Probab. 19 (2009), no. 1, 454--466. MR2498684
- A. Teixeira. Interlacement percolation on transient weighted graphs. Electron. J. Probab., in press, also available at arXiv:0907.0316.
- A. Teixeira. On the size of a finite vacant cluster of random interlacements with small intensity. Preprint, also available at: http://www.math.ethz.ch/u/sznitman/preprints
- Windisch, David. Random walk on a discrete torus and random interlacements. Electron. Commun. Probab. 13 (2008), 140--150. MR2386070 (2008k:60249)
- Windisch, David. Random walks on discrete cylinders with large bases and random interlacements. Ann Probab., in press, also available at arXiv:0907.1627.

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