Condensation transition in joint large deviations of linear statistics

Juraj Szavits-Nossan 1 Martin R. Evans 1 Satya N. Majumdar 2

Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2014, 47, pp.455004

Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states that the condensation can be understood in terms of sums of independent and identically distributed random variables: these exhibit condensation when they are conditioned to a large deviation of their sum. It is well understood that the condensation, whereby one of the random variables contributes a finite fraction to the sum, occurs only if the underlying probability distribution (modulo exponential) is heavy-tailed, i.e. decaying slower than exponential. Here we study a similar phenomenon in which condensation is exhibited for non-heavy-tailed distributions, provided random variables are additionally conditioned on a large deviation of certain linear statistics. We provide a detailed theoretical analysis explaining the phenomenon, which is supported by Monte Carlo simulations (for the case where the additional constraint is the sample variance) and demonstrated in several physical systems. Our results suggest that the condensation is a generic phenomenon that pertains to both typical and rare events.

  • 1. SUPA, School of Physics, University of Edinburgh
  • 2. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
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