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References

  1. N. Alon, I. Benjamini, A. Stacey. Percolation on finite graphs and isoperimetric inequalities. Ann. Probab., 32, (2004) 3, 1727-1745. Math. Review 2005f:05149
  2. I. Benjamini, A.S. Sznitman. Giant component and vacant set for random walk on a discrete torus. J. Eur. Math. Soc., 10 (2008) 1, 1-40. Math. Review 2008i:60076
  3. C.M. Fortuin, P.W. Kasteleyn, J. Ginibre. Correlation inequalities on some partially ordered sets. Comm. Math. Phys., 22 (1971) 89-103. Math. Review 46 #8607
  4. A. Dembo, A.S. Sznitman. On the disconnection of a discrete cylinder by a random walk. Probab. Theory Relat. Fields, 136 (2006) 2, 321-340. Math. Review 2007i:60053
  5. G. Grimmett. Percolation, Springer Verlag. second edition (1999). Math. Review 2001a:60114
  6. G. Grimmett, D. Stirzaker. Probability and random processes. Clarendon Press, Oxford, second edition (1992). Math. Review 93m:60002
  7. G.A. Hunt. Markoff chains and Martin boundaries. Illinoiws J. Math., 4 (1960) 313-340. Math. Review 23 #A691
  8. H. Kesten. Asymptotics in high dimensions for percolation. Disorder in physical systems: A volume in honour of John Hammersley (ed. G. Grimmett and D. J. A. Welsh), Clarendon Press, Oxford (1990) 219-240. Math. Review 91k:60114
  9. G.F. Lawler. Intersections of random walks. Birkhäuser (1991). Math. Review 92f:60122
  10. T.M. Liggett. Interacting Particle Systems. Springer Verlag (2005). Math. Review 2006b:60003
  11. V. Sidoravicius, A.S. Sznitman. Percolation for the vacant set of random interlacements. Comm. Pure Appl. Math., 62 (6) (2009), 831-858. Math. Review number not available.
  12. M.L. Silverstein. Symmetric Markov process. Lecture Notes in Math. 426, Springer Verlag, (1974). Math. Review 52 #6891
  13. A.S. Sznitman. How universal are asymptotics of disconnection times in discrete cylinders. Ann. Probab., 36 (2008) 1, 1-53. Math. Review 2008m:60143
  14. A.S. Sznitman. Vacant set of random interlacements and percolation. Accepted for publication in the Annals of Mathematics. Preprint available at www.math.ethz.ch/u/sznitman/ (2007).
  15. A.S. Sznitman. Random walks on discrete cylinders and random interlacements. Probab. Theory Relat. Fields, 145 (2009) 143-174. Math. Review number not available.
  16. A.S. Sznitman. Upper bound on the disconnection time of discrete cylinders and random interlacements . Accepted for publication in the Annals of Probability. Preprint available at www.math.ethz.ch/u/sznitman/ (2008).
  17. S.I. Resnick. Extreme Values, regular variation and point processes. Springer Verlag, (1987). Math. Review 89b:60241
  18. M. Watkins. Infinite paths that contain only shortest paths. Journ. of Combinat. Theory, 41 (1986) 341-355. Math. Review 87m:05118
  19. M. Weil. Quasi-processus. Séminaire de Probabilités IV, Lecture Notes in Math. 124, Springer Verlag, 217-239 (1970). Math. Review 42 #1212
  20. D. Windisch. Random walk on a discrete torus and random interlacements. Electron. Commun. Probab. 13 (2008), 140-150. Math. Review 2008k:60249
  21. W. Woess. Random walks on infinite graphs and groups. Cambridge University Press (2000). Math. Review 2001k:60006


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