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Parabolic and Hyperbolic Unimodular maps

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Random Geometry

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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