Rate of Convergence for Cardy's Formula

Dana Mendelson; Asaf Nachmias; Samuel S. Watson

doi:10.1007/s00220-014-2043-8

Rate of Convergence for Cardy's Formula

Dana Mendelson, Asaf Nachmias, Samuel S. Watson

Research output: Contribution to journal › Article › peer-review

Abstract

We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy-Smirnov formula. We use this result to obtain new upper and lower bounds of (Formula Presented) for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R ^-1/3+o(1).

Original language	English
Pages (from-to)	29-56
Number of pages	28
Journal	Communications in Mathematical Physics
Volume	329
Issue number	1
DOIs	https://doi.org/10.1007/s00220-014-2043-8
State	Published - Jul 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-014-2043-8

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title = "Rate of Convergence for Cardy's Formula",

abstract = "We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy-Smirnov formula. We use this result to obtain new upper and lower bounds of (Formula Presented) for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R -1/3+o(1).",

author = "Dana Mendelson and Asaf Nachmias and Watson, \{Samuel S.\}",

year = "2014",

month = jul,

doi = "10.1007/s00220-014-2043-8",

language = "الإنجليزيّة",

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journal = "Communications in Mathematical Physics",

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publisher = "Springer New York",

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T1 - Rate of Convergence for Cardy's Formula

AU - Mendelson, Dana

AU - Nachmias, Asaf

AU - Watson, Samuel S.

PY - 2014/7

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N2 - We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy-Smirnov formula. We use this result to obtain new upper and lower bounds of (Formula Presented) for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R -1/3+o(1).

AB - We show that crossing probabilities in 2D critical site percolation on the triangular lattice in a piecewise analytic Jordan domain converge with power law rate in the mesh size to their limit given by the Cardy-Smirnov formula. We use this result to obtain new upper and lower bounds of (Formula Presented) for the probability that the cluster at the origin in the half-plane has diameter R, improving the previously known estimate of R -1/3+o(1).

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U2 - 10.1007/s00220-014-2043-8

DO - 10.1007/s00220-014-2043-8

M3 - مقالة

SN - 0010-3616

VL - 329

SP - 29

EP - 56

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -

Rate of Convergence for Cardy's Formula

Abstract

All Science Journal Classification (ASJC) codes

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