The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Belius, David. Gumbel fluctuations for cover times in the discrete torus. Probab. Theory Related Fields 157 (2013), no. 3-4, 635--689. MR3129800
  • Benjamini, Itai; Sznitman, Alain-Sol. Giant component and vacant set for random walk on a discrete torus. J. Eur. Math. Soc. (JEMS) 10 (2008), no. 1, 133--172. MR2349899
  • van den Berg, M.; Bolthausen, E.; den Hollander, F. Moderate deviations for the volume of the Wiener sausage. Ann. of Math. (2) 153 (2001), no. 2, 355--406. MR1829754
  • Cerf, Raphaël. Large deviations for three dimensional supercritical percolation. Astérisque No. 267 (2000), vi+177 pp. MR1774341
  • Černý, Jiří; Teixeira, Augusto; Windisch, David. Giant vacant component left by a random walk in a random $d$-regular graph. Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011), no. 4, 929--968. MR2884219
  • Demuth, Michael; van Casteren, Jan A. Stochastic spectral theory for selfadjoint Feller operators. A functional integration approach. Probability and its Applications. Birkhäuser Verlag, Basel, 2000. xii+463 pp. ISBN: 3-7643-5887-4 MR1772266
  • Deuschel, Jean-Dominique; Stroock, Daniel W. Large deviations. Pure and Applied Mathematics, 137. Academic Press, Inc., Boston, MA, 1989. xiv+307 pp. ISBN: 0-12-213150-9 MR0997938
  • Ethier, Stewart N.; Kurtz, Thomas G. Markov processes. Characterization and convergence. Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1986. x+534 pp. ISBN: 0-471-08186-8 MR0838085
  • Fukushima, Masatoshi; Oshima, Yoichi; Takeda, Masayoshi. Dirichlet forms and symmetric Markov processes. Second revised and extended edition. de Gruyter Studies in Mathematics, 19. Walter de Gruyter & Co., Berlin, 2011. x+489 pp. ISBN: 978-3-11-021808-4 MR2778606
  • Grimmett, Geoffrey. Percolation. Second edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 321. Springer-Verlag, Berlin, 1999. xiv+444 pp. ISBN: 3-540-64902-6 MR1707339
  • 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
  • Lawler, Gregory F.; Limic, Vlada. Random walk: a modern introduction. Cambridge Studies in Advanced Mathematics, 123. Cambridge University Press, Cambridge, 2010. xii+364 pp. ISBN: 978-0-521-51918-2 MR2677157
  • X. Li and A.S. Sznitman. Large deviations for occupation time profiles of random interlacements. To appear in Probab. Theory Relat. Fields, also available at arXiv:1304.7477.
  • S. Popov and A. Teixeira. Soft local times and decoupling of random interlacements. To appear in J. Eur. Math. Soc., also available at arXiv:1212.1605.
  • Port, Sidney C.; Stone, Charles J. Brownian motion and classical potential theory. Probability and Mathematical Statistics. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. xii+236 pp. ISBN: 0-12-561850-6 MR0492329
  • Resnick, Sidney I. Extreme values, regular variation, and point processes. Applied Probability. A Series of the Applied Probability Trust, 4. Springer-Verlag, New York, 1987. xii+320 pp. ISBN: 0-387-96481-9 MR0900810
  • Sidoravicius, Vladas; Sznitman, Alain-Sol. Percolation for the vacant set of random interlacements. Comm. Pure Appl. Math. 62 (2009), no. 6, 831--858. MR2512613
  • Sidoravicius, Vladas; Sznitman, Alain-Sol. Connectivity bounds for the vacant set of random interlacements. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 4, 976--990. MR2744881
  • Sznitman, Alain-Sol. On the domination of random walk on a discrete cylinder by random interlacements. Electron. J. Probab. 14 (2009), no. 56, 1670--1704. MR2525107
  • Sznitman, Alain-Sol. Vacant set of random interlacements and percolation. Ann. of Math. (2) 171 (2010), no. 3, 2039--2087. MR2680403
  • Sznitman, Alain-Sol. Decoupling inequalities and interlacement percolation on $G\times\Bbb Z$. Invent. Math. 187 (2012), no. 3, 645--706. MR2891880
  • Sznitman, Alain-Sol. An isomorphism theorem for random interlacements. Electron. Commun. Probab. 17 (2012), no. 9, 9 pp. MR2892408
  • Teixeira, Augusto; Windisch, David. On the fragmentation of a torus by random walk. Comm. Pure Appl. Math. 64 (2011), no. 12, 1599--1646. MR2838338

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