APPROXIMATE UPPER-BOUNDS FOR THE CRITICAL PROBABILITY OF ORIENTED PERCOLATION IN 2 DIMENSIONS BASED ON RAPIDLY MIXING MARKOV-CHAINS

Authors
BOLLABAS B STACEY A
Citation
B. Bollabas et A. Stacey, APPROXIMATE UPPER-BOUNDS FOR THE CRITICAL PROBABILITY OF ORIENTED PERCOLATION IN 2 DIMENSIONS BASED ON RAPIDLY MIXING MARKOV-CHAINS, Journal of Applied Probability, 34(4), 1997, pp. 859-867
Citations number
16
Journal title
Journal of Applied Probability → ACNP
ISSN journal
00219002
Volume
34
Issue
4
Year of publication
1997
Pages
859 - 867
Database
ISI
SICI code
0021-9002(1997)34:4<859:AUFTCP>2.0.ZU;2-5
Abstract
We develop a technique for establishing statistical tests with precise confidence levels for upper bounds on the critical probability in ori ented percolation. We use it to give p(c) < 0.647 with a 99.999967% co nfidence. As Monte Carlo simulations suggest that p(c) approximate to 0.6445, this bound is fairly tight.