Crossing probability and number of crossing clusters in off-critical percolation
نویسندگان
چکیده
منابع مشابه
Universality of the excess number of clusters and the crossing probability function in three-dimensional percolation
Extensive Monte-Carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three-dimensional percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and bodycentered cubic (b.c.c.) lattices. Systems L × L × L′ with L′ >> L were studied for both bond (s.c., f.c.c., b.c.c.) and site (f.c.c.) percolation. The excess number of ...
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Langlands et al. considered two crossing probabilities, π h and π hv , in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of π h by treating it as a correlation function of boundary operators in the Q → 1 limit of the Q state Potts model. We extend his results to find an analogous formula for π hv which compares very well...
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Shape-dependent universal crossing probabilities are studied, via Monte Carlo simulations, for bond and site directed percolation on the square lattice in the diagonal direction, at the percolation threshold. In a dynamical interpretation, the crossing probability is the probability that, on a system with size L, an epidemic spreading without immunization remains active at time t. Since the sys...
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The logarithmic conformal field theory describing critical percolation is further explored using Watts’ determination of the probability that there exists a cluster connecting both horizontal and vertical edges. The boundary condition changing operator which governs Watts’ computation is identified with a primary field which does not fit naturally within the extended Kac table. Instead a “shift...
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The crossing number crðGÞ of a graph G is the minimum possible number of edge crossings in a drawing of G in the plane, while the pair-crossing number pcrðGÞ is the smallest number of pairs of edges that cross in a drawing of G in the plane. While crðGÞXpcrðGÞ holds trivially, it is not known whether a strict inequality can ever occur (this question was raised by Mohar and Pach and Tóth). We ai...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2011
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/3/032005