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Universal fluctuations in a simple disordered system

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)461 - 464
Number of pages4
JournalPhysics letters a
Volume160
Issue number5
DOIs
Publication statusPublished - 1991

Abstract

The mapping Li=1+xiLi-1 is studied. The xi, i=1, 2, 3, are independent random variables with common distribution. This mapping describes growth under fluctuating conditions, as may occur, e.g., in biology and economics. It also shows up in the grand canonical description of a directed polymer, bound to a wall of a random (1+1)-dimensional medium, in the limit where the polymer length goes to infinity. It is proven here that there is no self-averaging in this ?thermodynamic? limit. Distribution functions which show this behavior explicitly are derived.

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