Random Walk on Random Infinite Looptrees

Jakob E. Björnberg*, Sigurdur Örn Stefánsson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

Looptrees have recently arisen in the study of critical percolation on the uniform infinite planar triangulation. Here we consider random infinite looptrees defined as the local limit of the looptree associated with a critical Galton–Watson tree conditioned to be large. We study simple random walk on these infinite looptrees by means of providing estimates on volume and resistance growth. We prove that if the offspring distribution of the Galton–Watson process is in the domain of attraction of a stable distribution with index (Formula presented.) then the spectral dimension of the looptree is (Formula presented.).

Original languageEnglish
Pages (from-to)1234-1261
Number of pages28
JournalJournal of Statistical Physics
Volume158
Issue number6
DOIs
Publication statusPublished - Mar 2015

Bibliographical note

Funding Information:
Research supported by the Knut and Alice Wallenberg Foundation.

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Other keywords

  • Looptrees
  • Random trees
  • Random walk
  • Spectral dimension

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