Theorems on large deviations in the scheme of allocating identical particles into different cells

Theorems on large deviations in the scheme of allocating identical particles into different cells -- One-dimensional local and integral theorems on large deviations for the number of cells with a fixed number r of particles in the scheme of allocating n identical particles into N different cells, as n, N --» oo in the central domain, are obtained. We consider the scheme of allocating n particles into TV cells, where all allocations of particles into cells have the same probability ( n *^~ 1 ) . This scheme is mentioned in [1] as the Bose-Einstein statistics. Such a kind of allocation is considered in [2] in detail, where some limit theorems on distributions of random variables £r(n, TV), r = 0,1,..., are formulated and proved. Here £ r (n,TV) is the number of cells containing exactly r particles. The classification of possible domains of variation of n, TV and results of investigation of the limit distributions of the random variables £ r (n, TV) in these domains are presented in [3]. In this paper we obtain local and integral theorems on large deviations which give us the asymptotic estimates of the probabilities P{6-(n,TV) = &}, P{£ r (n,TV) > k} and P{£ r (n,TV) < k} in the central domain [4] of http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics and Applications de Gruyter

Theorems on large deviations in the scheme of allocating identical particles into different cells

Loading next page...
 
/lp/de-gruyter/theorems-on-large-deviations-in-the-scheme-of-allocating-identical-QkXOkJHWVf
Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0924-9265
eISSN
1569-3929
DOI
10.1515/dma.1993.3.6.635
Publisher site
See Article on Publisher Site

Abstract

-- One-dimensional local and integral theorems on large deviations for the number of cells with a fixed number r of particles in the scheme of allocating n identical particles into N different cells, as n, N --» oo in the central domain, are obtained. We consider the scheme of allocating n particles into TV cells, where all allocations of particles into cells have the same probability ( n *^~ 1 ) . This scheme is mentioned in [1] as the Bose-Einstein statistics. Such a kind of allocation is considered in [2] in detail, where some limit theorems on distributions of random variables £r(n, TV), r = 0,1,..., are formulated and proved. Here £ r (n,TV) is the number of cells containing exactly r particles. The classification of possible domains of variation of n, TV and results of investigation of the limit distributions of the random variables £ r (n, TV) in these domains are presented in [3]. In this paper we obtain local and integral theorems on large deviations which give us the asymptotic estimates of the probabilities P{6-(n,TV) = &}, P{£ r (n,TV) > k} and P{£ r (n,TV) < k} in the central domain [4] of

Journal

Discrete Mathematics and Applicationsde Gruyter

Published: Jan 1, 1993

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off