Random permutations: the general parametric model

We suggest a new approach to the study of the structural properties of random permutations based on defining some general parametric measure on the set $S_n$ of all permutations of degree $n$ which assigns to a permutation with cyclic structure $a=(a_1,\dots,a_n)$ the probability proportional to $\prod_{i=1}^n\theta_i^{a_i}$, where $\theta=(\theta_1,\dots,\theta_n)$ is a parameter of the measure.