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Bulletin of the American Mathematical Society

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Book Review

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Full text of review: PDF
Book Information:

Author: Harry Kesten
Title: Percolation theory for mathematicians
Additional book information: Progress in Probability and Statistics, vol. 2, Birkhauser, Boston, Mass., 1982, 423 pp., $30.00. ISBN 3-7643-3107-0.

References [Enhancements On Off] (What's this?)

  • 1. S. R. Broadbent and J. M. Hammersley, Percolation processes. I. Crystals and mazes, Proc. Cambridge Philos. Soc. 53 (1957), 629–641. MR 0091567
  • 2. J. M. Hammersley and D. J. A. Welsh, First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory, Proc. Internat. Res. Semin., Statist. Lab., Univ. California, Berkeley, Calif., Springer-Verlag, New York, 1965, pp. 61–110. MR 0198576
  • 3. T. E. Harris, A lower bound for the critical probability in a certain percolation process, Proc. Cambridge Philos. Soc. 56 (1960), 13–20. MR 0115221
  • 4. Harry Kesten, The critical probability of bond percolation on the square lattice equals 1\over2, Comm. Math. Phys. 74 (1980), no. 1, 41–59. MR 575895
  • 5. P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice, Ann. Discrete Math. 3 (1978), 227–245. Advances in graph theory (Cambridge Combinatorial Conf., Trinity College, Cambridge, 1977). MR 0494572
  • 6. R. T. Smythe and John C. Wierman, First-passage percolation on the square lattice, Lecture Notes in Mathematics, vol. 671, Springer, Berlin, 1978. MR 513421
  • 7. M. F. Sykes and J. W. Essam, Exact critical percolation probabilities for site and bond problems in two dimensions, J. Mathematical Phys. 5 (1964), 1117–1127. MR 0164680
  • 8. John C. Wierman, Bond percolation on honeycomb and triangular lattices, Adv. in Appl. Probab. 13 (1981), no. 2, 298–313. MR 612205, 10.2307/1426685

Review Information:

Reviewer: John C. Wierman
Journal: Bull. Amer. Math. Soc. 11 (1984), 404-409