Self-avoiding walks on finite graphs of large girth

Ariel Yadin

doi:10.30757/alea.v13-21

Self-avoiding walks on finite graphs of large girth

Ariel Yadin

Department of Mathematics

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

7 Scopus citations

Abstract

We consider self-avoiding walk on finite graphs with large girth. We study a few aspects of the model originally considered by Lawler, Schramm and Werner on finite balls in Z^d. The expected length of a random self avoiding path is considered. We discuss possible definitions of "critical" behavior in the finite volume setting. We also define a "critical exponent" γ for sequences of graphs of size tending to infinity, and show that γ= 1 in the large girth case.

Original language	English
Pages (from-to)	521-544
Number of pages	24
Journal	Alea
Volume	13
Issue number	2
DOIs	https://doi.org/10.30757/alea.v13-21
State	Published - 1 Jan 2016

Keywords

Critical exponents
Large girth graphs
Self-avoiding walk

ASJC Scopus subject areas

Statistics and Probability

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10.30757/alea.v13-21

Cite this

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AB - We consider self-avoiding walk on finite graphs with large girth. We study a few aspects of the model originally considered by Lawler, Schramm and Werner on finite balls in Zd. The expected length of a random self avoiding path is considered. We discuss possible definitions of "critical" behavior in the finite volume setting. We also define a "critical exponent" γ for sequences of graphs of size tending to infinity, and show that γ= 1 in the large girth case.

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KW - Self-avoiding walk

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Self-avoiding walks on finite graphs of large girth

Abstract

Keywords

ASJC Scopus subject areas

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