Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains

Journal of Applied Probability

Volumn 34, Issue 4, 1997, Pages 859-867

  Bollabás, Béla ^a   Stacey, Alan ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Computer algorithm; Coupling; Percolation; Rapid mixing

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; GRAPH THEORY; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; SET THEORY; STATISTICAL TESTS; TWO DIMENSIONAL;

DIRECTED GRAPH; ORIENTED PERCOLATION;

PROBABILITY;

EID: 0031295397     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200101573     Document Type: Article

References (15)

1. BALISTER, P., BOLLOBÁS, B. AND STACEY, A. (1993) Upper bounds for the critical probability of oriented percolation in two dimensions. Proc. R. Soc. London A 440, 201-220.
2. BALISTER, P., BOLLOBÁS, B. AND STACEY, A. (1994) Improved upper bounds for the critical probability of oriented percolation in two dimensions. Rand. Struct. Alg. 5, 573-589.
3. BROADBENT, S. R. AND HAMMERSLEY, J. M. (1957) Percolation processes I, II. Proc. Camb. Phil. Soc. 53, 629-641, 642-645.
4. DHAR, D.(1982) Percolation in two and three dimensions I. J. Phys. A 15, 1849-1858.
5. DHAR, D. AND BARMA, M. (1981) Monte Carlo simulation of directed percolation on a square lattice. J. Phys. C. 14, L1-L6.
6. DURRETT, R. (1984) Oriented percolation in two dimensions. Ann. Prob. 12, 999-1040.
7. DURRETT, R. (1988) Lecture Notes on Particle Systems and Percolation. Wadsworth and Brooks/Cole, New York.
8. DURRETT, R. (1992) Stochastic growth models: bounds on critical values. J. Appl. Prob. 29, 11-20.
9. GRIMMETT, G. (1989) Percolation. Springer, New York.
10. HARRIS, T. E. (1960) A lower bound for the critical probability in a certain percolation process. Proc. Camb. Phil. Soc. 56, 13-20.
11. KESTEN, H. (1980) The critical probability of bond percolation on the square lattice equals 1/2. Commun. Math. Phys. 74, 41-59.
12. LIGGETT, T. M. (1995) Survival of discrete time growth models, with applications to oriented percolation. Ann. Appl. Prob. 5, 613-636.
13. RUSSO, L. (1978) A note on percolation. Z. Wahrscheinlichkeitsth. 43, 39-48.
14. SEYMOUR, P. D. AND WELSH, D. J. A. (1978) Percolation probabilities on the square lattice. In Advances in Graph Theory. ed. B. Bollobás. North-Holland, Amsterdam. pp. 227-245.
15. STACEY, A. M. (1994) Bounds on the critical probability in oriented percolation models. PhD thesis. University of Cambridge.