Square permutations are typically rectangular

We describe the limit (for two topologies) of large uniform random square permutations, i.e.permutations where every point is a record.  First we describe the global behavior by showing these permutations have a permuton limit which can be described by a random rectangle.  We also explore fluctuations about this random rectangle, which we can describe through coupled Brownian motions.  Second, we consider the limiting behavior of the neighborhood of a point in the permutation through local limits. This is a joint work with E.Slivken

Slides (PDF)


ETH Zürich (Switzerland), Graduate seminar of probability.

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