Two-Stage Allocations and the Double $Q$-Function

Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1/N$. Let the $i$th cell contain $m_i$ partic...

Full description

Saved in:
Bibliographic Details
Published in:The Electronic journal of combinatorics 2003-05, Vol.10 (1)
Main Author: Agievich, Sergey
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c219t-f9779c1280bc2fdc446fe9cc2e58ce71ed5334ee605c9a3b14e8b3ac8123d2023
cites
container_end_page
container_issue 1
container_start_page
container_title The Electronic journal of combinatorics
container_volume 10
creator Agievich, Sergey
description Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1/N$. Let the $i$th cell contain $m_i$ particles on completion. Then associate with this cell the probability $a_i=m_i/m$ and withdraw the particles.2. The other $n$ particles are then allocated polynomially, that is, the probability of a particle falling into the $i$th cell is $a_i$.Let $\nu=\nu(m,N)$ be the number of the first particle that falls into a non-empty cell during the second stage. We give exact and asymptotic expressions for the expectation ${\bf E}\nu$.
doi_str_mv 10.37236/1714
format article
fullrecord <record><control><sourceid>crossref</sourceid><recordid>TN_cdi_crossref_primary_10_37236_1714</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_37236_1714</sourcerecordid><originalsourceid>FETCH-LOGICAL-c219t-f9779c1280bc2fdc446fe9cc2e58ce71ed5334ee605c9a3b14e8b3ac8123d2023</originalsourceid><addsrcrecordid>eNpNj8FKAzEURYMoWGv_IYu6jOa9ZCaTZalWhYKIdT1k3rxoZZzIZIr076XVhatz4cCFI8QM9LVxaMobcGBPxAS0c6ryWJ7-2-fiIucPrQG9LyYCNt9JvYzhjeWi6xKFcZv6LEPfyvGd5W3aNR3L-fNcrXY9HeSlOIuhyzz741S8ru42ywe1frp_XC7WihD8qKJ3zhNgpRvC2JK1ZWRPhFxUxA64LYyxzKUuyAfTgOWqMYEqQNOiRjMVV7-_NKScB47117D9DMO-Bl0fO-tDp_kBjJdC2A</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Two-Stage Allocations and the Double $Q$-Function</title><source>Freely Accessible Science Journals - check A-Z of ejournals</source><creator>Agievich, Sergey</creator><creatorcontrib>Agievich, Sergey</creatorcontrib><description>Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1/N$. Let the $i$th cell contain $m_i$ particles on completion. Then associate with this cell the probability $a_i=m_i/m$ and withdraw the particles.2. The other $n$ particles are then allocated polynomially, that is, the probability of a particle falling into the $i$th cell is $a_i$.Let $\nu=\nu(m,N)$ be the number of the first particle that falls into a non-empty cell during the second stage. We give exact and asymptotic expressions for the expectation ${\bf E}\nu$.</description><identifier>ISSN: 1077-8926</identifier><identifier>EISSN: 1077-8926</identifier><identifier>DOI: 10.37236/1714</identifier><language>eng</language><ispartof>The Electronic journal of combinatorics, 2003-05, Vol.10 (1)</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c219t-f9779c1280bc2fdc446fe9cc2e58ce71ed5334ee605c9a3b14e8b3ac8123d2023</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Agievich, Sergey</creatorcontrib><title>Two-Stage Allocations and the Double $Q$-Function</title><title>The Electronic journal of combinatorics</title><description>Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1/N$. Let the $i$th cell contain $m_i$ particles on completion. Then associate with this cell the probability $a_i=m_i/m$ and withdraw the particles.2. The other $n$ particles are then allocated polynomially, that is, the probability of a particle falling into the $i$th cell is $a_i$.Let $\nu=\nu(m,N)$ be the number of the first particle that falls into a non-empty cell during the second stage. We give exact and asymptotic expressions for the expectation ${\bf E}\nu$.</description><issn>1077-8926</issn><issn>1077-8926</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2003</creationdate><recordtype>article</recordtype><recordid>eNpNj8FKAzEURYMoWGv_IYu6jOa9ZCaTZalWhYKIdT1k3rxoZZzIZIr076XVhatz4cCFI8QM9LVxaMobcGBPxAS0c6ryWJ7-2-fiIucPrQG9LyYCNt9JvYzhjeWi6xKFcZv6LEPfyvGd5W3aNR3L-fNcrXY9HeSlOIuhyzz741S8ru42ywe1frp_XC7WihD8qKJ3zhNgpRvC2JK1ZWRPhFxUxA64LYyxzKUuyAfTgOWqMYEqQNOiRjMVV7-_NKScB47117D9DMO-Bl0fO-tDp_kBjJdC2A</recordid><startdate>20030512</startdate><enddate>20030512</enddate><creator>Agievich, Sergey</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20030512</creationdate><title>Two-Stage Allocations and the Double $Q$-Function</title><author>Agievich, Sergey</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c219t-f9779c1280bc2fdc446fe9cc2e58ce71ed5334ee605c9a3b14e8b3ac8123d2023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2003</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Agievich, Sergey</creatorcontrib><collection>CrossRef</collection><jtitle>The Electronic journal of combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Agievich, Sergey</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two-Stage Allocations and the Double $Q$-Function</atitle><jtitle>The Electronic journal of combinatorics</jtitle><date>2003-05-12</date><risdate>2003</risdate><volume>10</volume><issue>1</issue><issn>1077-8926</issn><eissn>1077-8926</eissn><abstract>Let $m+n$ particles be thrown randomly, independently of each other into $N$ cells, using the following two-stage procedure.1. The first $m$ particles are allocated equiprobably, that is, the probability of a particle falling into any particular cell is $1/N$. Let the $i$th cell contain $m_i$ particles on completion. Then associate with this cell the probability $a_i=m_i/m$ and withdraw the particles.2. The other $n$ particles are then allocated polynomially, that is, the probability of a particle falling into the $i$th cell is $a_i$.Let $\nu=\nu(m,N)$ be the number of the first particle that falls into a non-empty cell during the second stage. We give exact and asymptotic expressions for the expectation ${\bf E}\nu$.</abstract><doi>10.37236/1714</doi></addata></record>
fulltext fulltext
identifier ISSN: 1077-8926
ispartof The Electronic journal of combinatorics, 2003-05, Vol.10 (1)
issn 1077-8926
1077-8926
language eng
recordid cdi_crossref_primary_10_37236_1714
source Freely Accessible Science Journals - check A-Z of ejournals
title Two-Stage Allocations and the Double $Q$-Function
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T09%3A17%3A36IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Two-Stage%20Allocations%20and%20the%20Double%20$Q$-Function&rft.jtitle=The%20Electronic%20journal%20of%20combinatorics&rft.au=Agievich,%20Sergey&rft.date=2003-05-12&rft.volume=10&rft.issue=1&rft.issn=1077-8926&rft.eissn=1077-8926&rft_id=info:doi/10.37236/1714&rft_dat=%3Ccrossref%3E10_37236_1714%3C/crossref%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c219t-f9779c1280bc2fdc446fe9cc2e58ce71ed5334ee605c9a3b14e8b3ac8123d2023%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true