Inhomogeneous Percolation on Ladder Graphs

Reka Szabo*, Daniel Valesin

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We define an inhomogeneous percolation model on "ladder graphs" obtained as direct products of an arbitrary graph G=(V,E) and the set of integers Z (Vertices are thought of as having a "vertical" component indexed by an integer.) We make two natural choices for the set of edges, producing an unoriented graph G and an oriented graph G -> These graphs are endowed with percolation configurations in which independently, edges inside a fixed infinite "column" are open with probability q and all other edges are open with probability p. For all fixed q one can define the critical percolation threshold pc(q) We show that this function is continuous in (0, 1).

Original languageEnglish
Pages (from-to)992-1010
Number of pages19
JournalJournal of theoretical probability
Volume33
Issue number2
DOIs
Publication statusPublished - Jun-2020

Keywords

  • Inhomogeneous percolation
  • Oriented percolation
  • Ladder graphs
  • Critical parameter

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