2014/05/01 by Aernout C. D. van Enter, van Enter, Aernout C. D.
Mathematics · Physics and Astronomy · #60K35 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:60K35 #msc:82B43
paper · pdf · doi:10.48550/arxiv.1405.0152
Contribution to the proceedings of the 2013 EURANDOM workshop Probabilistic Cellular Automata: Theory, Applications and Future Perspectives, equation typo corrected, constant of generalisation corrected
arxiv created 2015/02/03 · arxiv updated 2015/02/04
In bootstrap percolation it is known that the critical percolation threshold tends to converge slowly to zero with increasing system size, or, inversely, the critical size diverges fast when the percolation probability goes to zero. To obtain higher-order terms (that is, sharp and sharper thresholds) for the percolation threshold in general is a hard question. In the case of two-dimensional anisotropic models, sometimes correction terms can be obtained from inversion in a relatively simple manner.