Colloquium Mathematics - Teun Verstraaten, University of Groningen

Titel: Asymptotic Behavior of Mallows Random Permutations

Abstract:

We study the asymptotics of permutations of {1,...,n} drawn at random according to the Mallows distribution. Under this distribution, each permutation \pi is selected with probability proportional to q^inv(\pi), where q>0 is a parameter and inv(\pi) denotes the number of i<j such that \pi(i) > \pi(j). We study the cycle counts of such random permutations when q is fixed. Also, given some first order sentence \phi we study the asymptotics of the probability that a Mallows permutation satisfies this sentence. We look at two natural classes of sentences for permutations.