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Parabolic and Hyperbolic Unimodular maps

Date: 
Friday 24th April 2015 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Co-authors: Tom Hutchcraft (UBC), Asaf Nachmias (Tel Aviv), Gourab Ray (Cambridge)

We show that for a unimodular random planar map, many geometric and probabilistic properties are equivalent. These include local and global properties: Negative mean curvature, invariant non-amenability, gap between the critical and uniqueness parameters for percolation, distinction between free and wired uniform spanning forests, and more.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons