{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T07:12:24Z","timestamp":1776582744164,"version":"3.51.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the asymptotic behavior of the following model: balls are sequentially thrown into bins so that the probability that a bin with $n$ balls obtains the next ball is proportional to $f(n)$ for some function $f$.  A commonly studied case where there are two bins and $f(n) = n^p$ for $p &gt; 1$.  In this case, one of the two bins eventually obtains a monopoly, in the sense that it obtains all balls thrown past some point.  This model is motivated by the phenomenon of positive feedback, where the \"rich get richer.\"  We derive a simple asymptotic expression for the probability that bin 1 obtains a monopoly when bin 1 starts with $x$ balls and bin 2 starts with $y$ balls for the case $f(n) = n^p$.  We then demonstrate the effectiveness of this approximation with some examples and demonstrate how it generalizes to a wide class of functions $f$.<\/jats:p>","DOI":"10.37236\/1784","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:22:29Z","timestamp":1578720149000},"source":"Crossref","is-referenced-by-count":8,"title":["A Scaling Result for Explosive Processes"],"prefix":"10.37236","volume":"11","author":[{"given":"M.","family":"Mitzenmacher","sequence":"first","affiliation":[]},{"given":"R.","family":"Oliveira","sequence":"additional","affiliation":[]},{"given":"J.","family":"Spencer","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,4,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:02:58Z","timestamp":1579323778000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,4,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1784","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,4,13]]},"article-number":"R31"}}