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math.PR2018
Oriented first passage percolation in the mean field limit, 2. The extremal process
Nicola Kistler, Adrien Schertzer, Marius A. Schmidt
This is the second, and last paper in which we address the behavior of oriented first passage percolation on the hypercube in the limit of large dimensions. We prove here that the…
math.PR2018
A Simple Proof of the DPRZ-Theorem for 2D Cover Times
Marius A. Schmidt
The purpose of these short notes is to provide a concise proof of a celebrated theorem by Dembo, Peres, Rosen and Zeitouni, which settles the leading order of cover times in the sm…
math.PR2018
First passage percolation in the mean field limit
Nicola Kistler, Adrien Schertzer, Marius A. Schmidt
The Poisson clumping heuristic has lead Aldous to conjecture the value of the first passage percolation on the hypercube in the limit of large dimensions. Aldous' conjecture has be…