The expected degree of minimal spanning forests
Probability
2013-06-04 v1 Functional Analysis
Group Theory
Abstract
We give a lower bound on the expected degree of the free minimal spanning forest of a vertex transitive graph in terms of its spectral radius. This result answers a question of Lyons-Peres-Schramm and simplifies the Gaboriau-Lyons proof of the measurable-group-theoretic solution to von Neumann's problem. In the second part we study a relative version of the free minimal spanning forest. As a consequence of this study we can show that non-torsion unitarizable groups have fixed price one.
Keywords
Cite
@article{arxiv.1306.0303,
title = {The expected degree of minimal spanning forests},
author = {Andreas Thom},
journal= {arXiv preprint arXiv:1306.0303},
year = {2013}
}
Comments
9 pages, no figures