Bulletin of the American Mathematical Society

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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.

S. R. Broadbent and J. M. Hammersley, Percolation processes. I. Crystals and mazes, Proc. Cambridge Philos. Soc. 53 (1957), 629–641. MR 91567, DOI 10.1017/s0305004100032680

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., 1963., Springer-Verlag, New York, 1965, pp. 61–110. MR 0198576

T. E. Harris, A lower bound for the critical probability in a certain percolation process, Proc. Cambridge Philos. Soc. 56 (1960), 13–20. MR 115221

Harry Kesten, The critical probability of bond percolation on the square lattice equals ${1\over 2}$, Comm. Math. Phys. 74 (1980), no. 1, 41–59. MR 575895

P. D. Seymour and D. J. A. Welsh, Percolation probabilities on the square lattice, Ann. Discrete Math. 3 (1978), 227–245. MR 494572

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

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 164680, DOI 10.1063/1.1704215

John C. Wierman, Bond percolation on honeycomb and triangular lattices, Adv. in Appl. Probab. 13 (1981), no. 2, 298–313. MR 612205, DOI 10.2307/1426685

1.

S. R. Broadbent and J. M. Hammersley (1957), Percolation processes, Proc. Cambridge Philos. Soc. 53, 629-641; 642-645. MR 0091567

2.

J. M. Hammersley and D. J. A. Welsh (1965), First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory, Bernoulli-Bayes-Laplace Anniversary Volume (J. Neyman and L. M. LeCam, eds.), Springer-Verlag, Berlin, pp. 61-110. MR 198576

3.

T. E. Harris (1960), A lower bound for the critical probability in a certain percolation process, Proc. Cambridge Philos. Soc. 56, 13-20. MR 115221

4.

H. Kesten (1980), The critical probability of bond percolation on the square lattice equals 1/2, Comm. Math. Phys. 74, 41-59. MR 575895

5.

P. D. Seymour and D. J. A. Welsh (1978), Percolation probabilities on the square lattice, Ann. Discrete Math. 3, 227-245. MR 494572

6.

R. T. Smythe and J. C. Wierman (1978), First-passage percolation on the square lattice, Lecture Notes in Math., vol. 671, Springer-Verlag. MR 513421

7.

M. F. Sykes and J. W. Essam (1964), Exact critical percolation probabilities for site and bond problems in two dimensions, J. Math. Phys. 5, 1117-1127. MR 164680

8.

J. C. Wierman (1981), Bond percolation on honeycomb and triangular lattices, Adv. in Appl. Probab. 13, 298-313. MR 612205