ON THE CYCLE STRUCTURE OF RANDOM PERMUTATIONS
Valerii Evgen'evich Tarakanov, V P Čistjakov · Mathematics of the USSR-Sbornik · 1975
Suppose a probability distribution is given on the set of all permutations of degree . The authors solve the problem of the joint distribution of the random variables , where is the number of cycles of length in a permutation from , in a series of cases, when the initial distribution is not uniform on all of but on certain special subsets of it. In these cases it is shown that in the limit as the random variables are independent and each of them has a Poisson distribution. Cases in which no joint limit distribution exists are also noted.Bibliography: 4 titles.