Limit theorems for allocation of particles over different cells with restrictions
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 712-725
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Equiprobable allocation schemes of $n$ indistinguishable or
distinguishable particles over $N$ distinguishable cells are
considered provided the fillings of the cells take on values in a
fixed subset $A$ of the set of nonnegative integers. Local normal
and Poisson theorems are proved for the distributions of the
number of cells, each of which contains exactly $r$ particles, and
for the number of cycles of length $r\in A$ in a permutation
selected at random and equiprobable from the set of all
permutations of order $n$ with $N$ cycles $(N\le n)$ whose
lengths are elements of a set $A\subsetN$. It is assumed that
$n,N\to\infty$ in the central domain.
Keywords:
random allocations, asymptotic expansions, saddle-point method, local normal theorem.
@article{TVP_2004_49_4_a4,
author = {A. N. Timashev},
title = {Limit theorems for allocation of particles over different cells with restrictions},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {712--725},
publisher = {mathdoc},
volume = {49},
number = {4},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a4/}
}
TY - JOUR AU - A. N. Timashev TI - Limit theorems for allocation of particles over different cells with restrictions JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2004 SP - 712 EP - 725 VL - 49 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a4/ LA - ru ID - TVP_2004_49_4_a4 ER -
A. N. Timashev. Limit theorems for allocation of particles over different cells with restrictions. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 4, pp. 712-725. http://geodesic.mathdoc.fr/item/TVP_2004_49_4_a4/