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References

  1. Antal, Peter; Pisztora, Agoston. On the chemical distance for supercritical Bernoulli percolation. Ann. Probab. 24 (1996), no. 2, 1036--1048. MR1404543 (98b:60168)
  2. Barlow, Martin T. Random walks on supercritical percolation clusters}, Ann. Probab. 32 (2004), no.4, 3024--3084.
  3. Berger, Noam; Biskup, Marek. Quenched invariance principle for simple random walk on percolation clusters. Probab. Theory Related Fields 137 (2007), no. 1-2, 83--120. MR2278453 (2007m:60085)
  4. Barlow, M. T.; Hambly, B. M. Parabolic Harnack inequality and local limit theorem for percolation clusters. Electron. J. Probab. 14 (2009), no. 1, 1--27. MR2471657 (2010b:60267)
  5. Delmotte, Thierry. Graphs between the elliptic and parabolic Harnack inequalities. Potential Anal. 16 (2002), no. 2, 151--168. MR1881595 (2003b:39019)
  6. Diaconis, P.; Fulton, W. A growth model, a game, an algebra, Lagrange inversion, and characteristic classes.Commutative algebra and algebraic geometry, II (Italian) (Turin, 1990). Rend. Sem. Mat. Univ. Politec. Torino 49 (1991), no. 1, 95--119 (1993). MR1218674 (94d:60105)
  7. Doyle, Peter G.; Snell, J. Laurie. Random walks and electric networks.Carus Mathematical Monographs, 22. Mathematical Association of America, Washington, DC, 1984. xiv+159 pp. ISBN: 0-88385-024-9 MR0920811 (89a:94023)
  8. Durrett, R.; Schonmann, R. H. Large deviations for the contact process and two-dimensional percolation. Probab. Theory Related Fields 77 (1988), no. 4, 583--603. MR0933991 (89i:60195)
  9. A. Gandolfi, Clustering and uniqueness in mathematical models of percolation phenomena, Ph.D. thesis, 1989.
  10. Lawler, Gregory F.; Bramson, Maury; Griffeath, David. Internal diffusion limited aggregation. Ann. Probab. 20 (1992), no. 4, 2117--2140. MR1188055 (94a:60105)
  11. Mathieu, P.; Piatnitski, A. Quenched invariance principles for random walks on percolation clusters. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 463 (2007), no. 2085, 2287--2307. MR2345229 (2008e:82033)
  12. Telcs, András. The art of random walks.Lecture Notes in Mathematics, 1885. Springer-Verlag, Berlin, 2006. viii+195 pp. ISBN: 978-3-540-33027-1; 3-540-33027-5 MR2240535 (2007d:60001)
  13. Varopoulos, Nicholas Th. Long range estimates for Markov chains. Bull. Sci. Math. (2) 109 (1985), no. 3, 225--252. MR0822826 (87j:60100)
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