Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T01:25:23.762Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniqueness in two-dimensional rigidity percolation

Published online by Cambridge University Press:  06 March 2001

OLLE HÄGGSTRÖM
OLLE HÄGGSTRÖM
Affiliation:
Mathematical Statistics, Chalmers University of Technology, 412 96 Göteborg, Sweden. e-mail: [email protected]://www.math.chalmers.se/~olleh/
Get access Rights & Permissions [Opens in a new window]

Abstract

For bond percolation on the two-dimensional triangular lattice with arbitrary retention parameter p ∈ [0, 1], we show that the number of infinite rigid components is a.s. at most 1. This proves a conjecture by Holroyd. Further results, concerning simultaneous uniqueness, and continuity (in p) of the probability that a given edge is in an infinite rigid component, are also obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 130 , Issue 1 , January 2001 , pp. 175 - 188
Copyright
2001 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)