Condensation and extreme value statistics

Martin R. Evans, Satya N. Majumdar

Research output: Contribution to journalArticlepeer-review

Abstract

We study the factorized steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density the marginal distribution for the mass at a single site develops a bump, p(cond)(m), at large mass m. This bump corresponds to a condensate site carrying a finite fraction of the mass in the system. Here, we study the condensation transition from a different aspect, that of extreme value statistics. We consider the cumulative distribution of the largest mass in the system and compute its asymptotic behaviour. We show three distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Frechet, and above the critical density a different distribution emerges. We relate p(cond)(m) to the probability density of the largest mass in the system.

Original languageEnglish
Article numberP05004
Pages (from-to)-
Number of pages11
Journal Journal of Statistical Mechanics: Theory and Experiment
DOIs
Publication statusPublished - May 2008

Keywords

  • stochastic particle dynamics (theory)
  • stationary states
  • zero-range processes
  • large deviations in non-equilibrium systems
  • FACTORIZED STEADY-STATES
  • MASS-TRANSPORT MODELS
  • ZERO-RANGE PROCESSES
  • PHASE-TRANSITIONS
  • PARTICLE-SYSTEMS
  • RANDOM MATRICES
  • FLUCTUATIONS
  • AGGREGATION
  • EIGENVALUE

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