This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible)… (More)

The number cn of weighted partitions of an integer n, with parameters (weights) bk, k ≥ 1, is given by the generating function relationship ∑∞ n=0 cnz n = ∏∞ k=1(1− zk)−bk . Meinardus(1954)… (More)

The coagulation-fragmentation process models the stochastic evolution of a population of N particles distributed into groups of different sizes that coagulate and fragment at given rates. The process… (More)

The paper is devoted to the estimation of the rate of of exponential convergence of nonhomogeneous queues exhibiting different types of ergodicity. The main tool of our study is the method, which was… (More)

We develop a unified approach to the problem of clustering in the three different fields of applications indicated in the title of the paper, in the case when the parametric function of the models is… (More)

A multiset is an unordered sample from a set of object types in which the number of items is variable, but the total weight of the objects equals a parameter n. The number of types of objects of… (More)

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the… (More)

We find limit shapes for a family of multiplicative measures on the set of partitions, induced by exponential generating functions with expansive parameters, ak ∼ Ck, k → ∞, p > 0, where C is a… (More)

We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence… (More)

We establish necessary and sufficient conditions for convergence of non scaled multiplicative measures on the set of partitions. The measures depict component spectrums of random structures and the… (More)