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On Near-critical and Dynamical Percolation in the Tree Case by Olle Häggström; Robin Pemantle is a Mathematics article available to read on EtoBox.

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Consider independent bond percolation with retention probability p on a Ž . spherically symmetric tree ⌫. Write p for the probability that the root is in an infinite ⌫ Ä Ž . 4 Ž . open cluster, and define the critical value p s inf p : p ) 0 . If p s 0, then the c ⌫ ⌫ c root may still percolate in the corresponding dynamical percolation process at the critical value p , as demonstrated recently by Haggstrom, Peres, and Steif. Here we relate this ̈c Ž . phenomenon to the near-critical behavior of p by showing that the root percolates in ⌫ 1 Ž Ž .. y1 the dynamical percolation process if and only if H p dp-ρ. The ''only if '' direction p ⌫ c extends to general trees, whereas the ''if '' direction fails in this generality.

Who reads On Near-critical and Dynamical Percolation in the Tree Case?

Author

Olle Häggström; Robin Pemantle

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1042-9832)

Published

1999

Language

EN

Field

Mathematics (Physical Sciences)