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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
First-passage percolation in random planar maps and Tutte's bijection
Thomas Lehéricy
We consider large random planar maps and study the first-passage percolation distance obtained by assigning independent identically distributed lengths to the edges. We consider th…