SR 000.03

## Seminar in probability theory: Marius Schmidt (Basel)

**Oriented first passage percolation on the hypercube**

Consider the hypercube as a graph with vertex set {0,1}^N and edges between two vertices if they are only one coordinate flip apart. Choosing independent standard exponentially distributed lengths for all edges and asking how long the shortest directed paths from (0,..,0) to (1,..,1) is defines oriented first passage percolation on the hypercube. We will discuss the conceptual steps needed to answer this question to the precision of extremal process following the two paper series "Oriented first passage percolation in the mean field limit" by Nicola Kistler, Adrien Schertzer and Marius A. Schmidt: arXiv:1804.03117 and arXiv:1808.04598.

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