A scaling result for explosive processes

M. Mitzenmacher, R. Oliveira, J. Spencer

Research output: Contribution to journalArticle

Abstract

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) = np for p > 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) = np. We then demonstrate the effectiveness of this approximation with some examples and demonstrate how it generalizes to a wide class of functions f.

Original languageEnglish (US)
JournalElectronic Journal of Combinatorics
Volume11
Issue number1 R
StatePublished - Apr 13 2004

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Bins
Ball
Scaling
Positive Feedback
Demonstrate
Asymptotic Behavior
Directly proportional
Generalise
Feedback
Approximation
Model

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

A scaling result for explosive processes. / Mitzenmacher, M.; Oliveira, R.; Spencer, J.

In: Electronic Journal of Combinatorics, Vol. 11, No. 1 R, 13.04.2004.

Research output: Contribution to journalArticle

Mitzenmacher, M. ; Oliveira, R. ; Spencer, J. / A scaling result for explosive processes. In: Electronic Journal of Combinatorics. 2004 ; Vol. 11, No. 1 R.
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