Condensation transition in joint large deviations of linear statistics

Abstract

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