Condensation transition in joint large deviations of linear statistics

Abstract

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.

30 pages, 4 figures (minor revision)

References in corpus (8)

• The large deviation approach to statistical mechanics
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Statistical distribution of quantum entanglement for a random bipartite state
• Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices
• Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process
• Condensation of Fluctuations in and out of Equilibrium
• Real-space Condensation in Stochastic Mass Transport Models

Cited by in corpus (7)

• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Participation ratio for constraint-driven condensation with superextensive mass
• Probability distributions with singularities
• Conditioned random walks and interaction-driven condensation
• Condensation of degrees emerging through a first-order phase transition in classical random graphs
• Condensation induced by coupled transport processes
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension