Random Uniform Permutations

Abstract : This course is at the interplay between Probability and Combinatorics. It is intended for Master students with a background in Probability (random variables, expectation, conditional probability). The question we will adress is ”What can we say about a typical large permutation?”: the number of cycles, their lengths, the number of fixed points,... This is also a pretext to present some universal phenomena in Probability: reinforcement, the Poisson paradigm, size-bias,...