Mean-field behavior for the survival probability and the percolation point-to-surface connectivity

A. Sakai

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)

Abstract

We consider the critical survival probability (up to timet) for oriented percolation and the contact process, and the point-to-surface (of the ball of radiust) connectivity for critical percolation. Let t denote both quantities. We prove in a unified fashion that, if t exhibits a power law and both the two-point function and its certain restricted version exhibit the same mean-field behavior, then t=t-1 for the time-oriented models with d > 4 and t=t-2 for percolation with d > 7.
Original languageEnglish
Pages (from-to)111-130
JournalJournal of Statistical Physics
Volume117
Issue number1-2
DOIs
Publication statusPublished - 2004

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