Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
-
A. N. Timashov
Abstract
We consider the mapping CN,n of a set with n numbered elements into itself, which has N ≤ n connected components and is uniformly distributed on the set of all such mappings. We denote the number of such mappings by a(n, N). In addition to the known estimates we derive some new estimates of the number a(n, N) under the condition that n → ∞ and N = N(n).
Let η1, . . . , ηN be the sizes of connected components of the random mapping CN,n, numbered in one of the N! possible ways. We obtain limit theorems estimating the distribution of the random vector (η1, . . . , ηN) as n, N →∞ including the domain of large deviations. A new asymptotic estimate of the local probabilities for a sum of independent identically distributed random variables which determine the corresponding generalised allocation scheme is obtained.
© de Gruyter 2011
Articles in the same Issue
- On the maximum size of a tree in a random unlabelled unrooted forest
- Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times
- Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
- A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences
- The critical ω-foliated τ-closed formations of finite groups
- On the semigroups of endomorphisms of direct products of commutative Moufang loops
- The Voronoi polyhedra of the rooted lattice E6 and of its dual lattice
- Calculation of the characteristic polynomial of a matrix
- A case of insolubility of the problem of equivalence of programs
Articles in the same Issue
- On the maximum size of a tree in a random unlabelled unrooted forest
- Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times
- Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
- A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences
- The critical ω-foliated τ-closed formations of finite groups
- On the semigroups of endomorphisms of direct products of commutative Moufang loops
- The Voronoi polyhedra of the rooted lattice E6 and of its dual lattice
- Calculation of the characteristic polynomial of a matrix
- A case of insolubility of the problem of equivalence of programs
