Boundary-connectivity via graph theory

Author:
Ádám Timár

Journal:
Proc. Amer. Math. Soc. **141** (2013), 475-480

MSC (2000):
Primary 05C10, 05C63; Secondary 20F65, 60K35

Published electronically:
June 21, 2012

MathSciNet review:
2996951

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Abstract | References | Similar Articles | Additional Information

Abstract: We generalize theorems of Kesten and Deuschel-Pisztora about the connectedness of the exterior boundary of a connected subset of , where ``connectedness'' and ``boundary'' are understood with respect to

various graphs on the vertices of . These theorems are widely used in statistical physics and related areas of probability. We provide simple and elementary proofs of their results. It turns out that the proper way of viewing these questions is graph theory instead of topology.

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Additional Information

**Ádám Timár**

Affiliation:
Hausdorff Center for Mathematics, Universität Bonn, D-53115 Bonn, Germany

Email:
adam.timar@hcm.uni-bonn.de

DOI:
http://dx.doi.org/10.1090/S0002-9939-2012-11333-4

Received by editor(s):
March 25, 2010

Received by editor(s) in revised form:
February 21, 2011, July 1, 2011, and July 5, 2011

Published electronically:
June 21, 2012

Communicated by:
Richard C. Bradley

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.