Continuum percolation with steps in the square or the disc

Random Structures and Algorithms

Volumn 26, Issue 4, 2005, Pages 392-403

  Balister, Paul ^a   Bollobás, Béla ^a,b   Walters, Mark ^a,b  

^a University of Memphis   (United States)

^b TRINITY COLLEGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22944433903     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.20064     Document Type: Article

References (28)

1. U. Alon, A. Drory, and I. Balberg, Phys Rev A (42) (1990), 4634-4638.
2. E. Andjel, Characteristic exponents for two-dimensional bootstrap percolation, Ann Probab 21 (1993), 926-935.
3. D. R. Baker, G. Paul, S. Sreenivasan, and H. E. Stanley, The critical percolation threshold for randomly oriented interpenetrating squares and cubes, Phys Rev E 66 (2002), 046136.
4. B. Bollobás, Random graphs, 2nd edition, Cambridge University Press, Cambridge, 2001.
5. B. Bollobás and A. Stacey, Approximate upper bounds for the critical probability of oriented percolation in two dimensions based on rapidly mixing Markov chains, J Appl Probab 34 (1997), 859-867.
6. C. Domb, A note on the series expansion method for clustering problems, Biometrika 59 (1972), 209.
7. M. A. Dubson and J. C. Garland, Measurement of the conductivity exponent in two-dimensional percolating networks: square lattice versus random-void continuum, Phys Rev B 32 (1985), 7621-7623.
8. R. Durrett, Lecture notes on particle systems and percolation, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1988.
9. A. Ermakov and J. van den Berg, A new lower bound for the critical probability of site percolation on the square lattice, Random Structures Algorithms 8 (1996), 19-214.
10. D. H. Fremlin, The clustering problem: some Monte Carlo results, J Physique 37 (1976), 813.
11. E. J. Garboczi, M. F. Thorpe, M. S. DeVries, and A. R. Day, Universal conductivity curve for a plane containing random holes, Phys Rev A 43 (1991), 6743.
12. E. N. Gilbert, Random plane networks, J Soc Indust Appl Math 9 (1961), 533-543.
13. G. R. Grimmett, Percolation, second edition, Springer, New York, 1999.
14. E. T. Gawlinski and H. E. Stanley, Continuum percolation in two dimensions: Monte Carlo tests of scaling and universality for non-interacting discs, J Phys A 14 (1981), L291-L299.
15. Gnu Scientific Library (Random Number Generators), http://sources.redhat.com/gsl/ref/gsl-ref_17.html
16. S. W. Haan and R. Zwanzig, Series expansions in a continuum percolation problem, J Phys A 10 (1977), 1547-1555.
17. P. R. King, The connectivity and conductivity of overlapping sandbodies, in: A. T. Buller, E. Berg, O. Hjelmeland, J. Kleppe, O. Torsaeter, J. O. Aasen (Editors), North Sea oil and gas Resevoirs - II, Graham and Trotman Inc., London, 1990, pp. 353-358.
18. T. M. Liggett, R. H. Schonmann, and A.M. Stacey, Domination by product measures, Ann Probab 25 (1997), 71-95.
19. B. Lorenz, I. Orgzall, and H.-O. Heuer, J Phys A 26 (1993), 4711.
20. R. Meester and R. Roy, Continuum percolation, Cambridge University Press, Cambridge, 1996.
21. G. E. Pike and C. H. Seager, Percolation and conductivity: A computer study. I, Phys Rev B 10 (1974), 1421-1434.
22. A. Pisztora, Surface order large deviations for Ising, Potts and percolation models, Probab Theory Related Fields 104 (1996), 427-466.
23. J. Quintanilla and S. Torquato, Percolation for a model of statistically inhomogeneous random media, J Chem Phys 111 (1999), 5947-5954.
24. J. Quintanilla, S. Torquato, and R. M. Ziff, Efficient measurement of the percolation threshold for fully penetrable discs, J Phys A 33(42) (2000), L399-L407.
25. F. D. K. Roberts, A Monte Carlo solution of a two-dimensional unstructured cluster problem, Biometrika 54 (1967), 625-628.
26. M. Rosso, Concentration gradient approach to continuum percolation in two dimensions, J Phys A 22 (1989), L131-L136.
27. J. Wierman, Substitution method critical probability bounds for the square lattice site percolation model, Combin Probab Comput 4, (1995), 181-188.
28. R. Ziff, Spanning probability in 2D percolation, Phys Rev Lett 69 (1992), 2670-2673.