Constraint-Driven Condensation in Large Fluctuations of Linear Statistics

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Abstract

Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in traffic, and gelation in networks. We show here that the same condensation scenario, which normally happens only if the underlying probability distribution has tails heavier than exponential, can occur for light-tailed distributions in the presence of additional constraints. We demonstrate this phenomenon on the sample variance, whose probability distribution conditioned on the particular value of the sample mean undergoes a phase transition. The transition is manifested by a change in behavior of the large deviation rate function.

Original languageEnglish
Article number020602
Number of pages5
JournalPhysical Review Letters
Volume112
Issue number2
Early online date14 Jan 2014
DOIs
Publication statusPublished - 17 Jan 2014

Keywords

  • ZERO-RANGE PROCESSES
  • CONDENSATION
  • LARGE DEVIATIONS

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