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arXiv · 1306.0303

The expected degree of minimal spanning forests

Andreas Thom
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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.

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Andreas Thom. 2013-06-03. The expected degree of minimal spanning forests. https://arxiv.org/abs/1306.0303

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