Asymptotic behavior of mallows random permutations

In this thesis we investigate Mallows(n,q) distributed random permutations as we let n go to infinity. For such permutations we give the limit distributions for the cycle counts, and investigate the existence of convergence and 0-1 laws in two different first-order logical theories. It turns out that the existence of such laws depends on q, we give a full description for the case that q does not depend on n.