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math.PR2019
Recurrence of the Uniform Infinite Half-Plane Map via duality of resistances
Thomas Budzinski, Thomas Lehéricy
We study the simple random walk on the Uniform Infinite Half-Plane Map, which is the local limit of critical Boltzmann planar maps with a large and simple boundary. We prove that t…
math.PR2019
Universality for random surfaces in unconstrained genus
Thomas Budzinski, Nicolas Curien, Bram Petri
Starting from an arbitrary sequence of polygons whose total perimeter is , we can build an (oriented) surface by pairing their sides in a uniform fashion. Chmutov and Pittel (a…