Essential Spanning Forests and Electrical Networks on Groups

Rita Solomyak ()
Additional contact information
Rita Solomyak: Tel Aviv University

Journal of Theoretical Probability, 1999, vol. 12, issue 2, 523-548

Abstract: Abstract Let Γ be a Cayley graph of a finitely generated group G. Subgraphs which contain all vertices of Γ, have no cycles, and no finite connected components are called essential spanning forests. The set $$Y$$ of all such subgraphs can be endowed with a compact topology, and G acts on $$Y$$ by translations. We define a “uniform” G-invariant probability measure μ on $$Y$$ show that μ is mixing, and give a sufficient condition for directional tail triviality. For non-cocompact Fuchsian groups we show how μ can be computed on cylinder sets. We obtain as a corollary, that the tail σ-algebra is trivial, and that the rate of convergence to mixing is exponential. The transfer-current function ψ (an analogue to the Green function), is computed explicitly for the Modular and Hecke groups.

Keywords: probability measure; Cayley graph; spanning forest; non-cocompact Fuchsian group (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1021638430098 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:12:y:1999:i:2:d:10.1023_a:1021638430098

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1021638430098

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().