Sharp metastability threshold for two-dimensional bootstrap percolation

Probability Theory and Related Fields

Volumn 125, Issue 2, 2003, Pages 195-224

  Holroyd, Alexander E ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bootstrap percolation; Cellular automaton; Finite size scaling; Metastability

Indexed keywords

EID: 0038270639     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-002-0239-x     Document Type: Article

References (24)

1. Adler, J.: Bootstrap percolation. Physica A, 171, 453-470 (1991)
2. Adler, J., Stauffer, D., Aharony, A.: Comparison of bootstrap percolation models. Journal of Physics A, 22, L297-L301 (1989)
3. Aizenman, M., Lebowitz, J.L.: Metastability effects in bootstrap percolation. J. Phys. A, 21(19), 3801-3813(1988)
4. Andjel, E.D., Mountford, T.S., Schonmann, R.H.: Equivalence of exponential decay rates for bootstrap-percolation-like cellular automata. Ann. Inst. H. Poincaré Probab. Statist., 31(1), 13-25 (1995)
5. Balogh, J., Bollobás, B.: Bootstrap percolation on the hypercube. To appear
6. Boas, M.L.: Mathematical Methods in the Physical Sciences. Wiley, second edition, 1983
7. Cerf, R., Cirillo, E.N.M.: Finite size scaling in three-dimensional bootstrap percolation. Ann. Probab., 27(4), 1837-1850 (1999)
8. Cerf, R., Manzo, F.: The threshold regime of finite volume bootstrap percolation. To appear
9. Fontes, L.R., Sidoravicius, V., Schonmann, R.H.: Stretched exponential fixation in stochastic Ising models at zero temperature. Communications in Mathematical Physics. To appear
10. Froböse, K.: Finite-size effects in a cellular automaton for diffusion. J. Statist. Phys., 55(5-6), 1285-1292 (1989)
11. Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals series and products. Academic Press, New York, 1965
12. 2. Ann. Probab., 24(4), 1752-1778 (1996)
13. Gravner, J., Griffeath, D.: Scaling laws for a class of critical cellular automaton growth rules. In Random walks (Budapest 1998), pages 167-186. János Bolyai Math. Soc., Budapest, 1999
14. Gravner, J., McDonald, E.: Bootstrap percolation in a polluted environment. J. Statist. Phys., 87(3-4), 915-927 (1997)
15. Grimmett, G.R.: Percolation. Springer-Verlag, second edition, 1999
16. Kirkpatrick, S., Wilcke, W., Garner, R., Huels, H.: Percolation in dense storage arrays. Physica A. To appear
17. Mountford, T.S.: Rates for the probability of large cubes being non-internally spanned in modified bootstrap percolation. Probab. Theory Related Fields, 93(2), 159-167 (1992)
18. Schonmann, R.H.: Finite size scaling behavior of a biased majority rule cellular automaton. Phys. A, 167(3), 619-627 (1990)
19. Schonmann, R.H.: On the behavior of some cellular automata related to bootstrap percolation. Ann. Probab., 20(1), 174-193 (1992)
20. Schonmann, R.H.: Slow droplet-driven relaxation of stochastic Ising models in the vicinity of the phase coexistence region. Comm. Math. Phys., 161(1), 1-49 (1994)
21. Schonmann, R.H., Shlosman, S.B.: Wulff droplets and the metastable relaxation of kinetic Ising models. Comm. Math. Phys., 194(2), 389-462 (1998)
22. van Enter, A.C.D., Adler, J., Duarte, J.A.M.S.: Finite-size effects for some bootstrap percolation models. J. Statist. Phys., 60(3-4), 323-332 (1990)
23. van Enter, A.C.D., Adler, J., Duarte, J.A.M.S.: Addendum: "Finite size effects for some bootstrap percolation models". J. Statist. Phys., 62(1-2), 505-506 (1991)
24. Wolfram, S.: editor. Theory and applications of cellular automata. World Scientific Publishing Co., Singapore, 1986. Including selected papers 1983-1986