On monochromatic arm exponents for 2D critical percolation

Vincent Beffara; Pierre Nolin

doi:10.1214/10-AOP581

On monochromatic arm exponents for 2D critical percolation

Vincent Beffara
, Pierre Nolin

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

32 Citations (Scopus)

Abstract

We investigate the so-called monochromatic arm exponents for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j +1)-arm exponents.

Original language	English
Pages (from-to)	1286-1304
Journal	Annals of Probability
Volume	39
Issue number	4
Online published	5 Aug 2011
DOIs	https://doi.org/10.1214/10-AOP581
Publication status	Published - 2011
Externally published	Yes

Research Keywords

Critical exponent
Percolation
Scaling limit

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title = "On monochromatic arm exponents for 2D critical percolation",

abstract = "We investigate the so-called monochromatic arm exponents for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j +1)-arm exponents. ",

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T1 - On monochromatic arm exponents for 2D critical percolation

AU - Beffara, Vincent

AU - Nolin, Pierre

PY - 2011

Y1 - 2011

N2 - We investigate the so-called monochromatic arm exponents for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j +1)-arm exponents.

AB - We investigate the so-called monochromatic arm exponents for critical percolation in two dimensions. These exponents, describing the probability of observing j disjoint macroscopic paths, are shown to exist and to form a different family from the (now well understood) polychromatic exponents. More specifically, our main result is that the monochromatic j-arm exponent is strictly between the polychromatic j-arm and (j +1)-arm exponents.

KW - Critical exponent

KW - Percolation

KW - Scaling limit

UR - https://www.scopus.com/pages/publications/80051620605

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-80051620605&origin=recordpage

U2 - 10.1214/10-AOP581

DO - 10.1214/10-AOP581

M3 - RGC 21 - Publication in refereed journal

SN - 0091-1798

VL - 39

SP - 1286

EP - 1304

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

On monochromatic arm exponents for 2D critical percolation

Abstract

Research Keywords

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