Condensation transition in joint large deviations of linear statistics

TL;DR

This paper investigates a condensation phenomenon in large deviations of linear statistics for non-heavy-tailed distributions, supported by theoretical analysis and Monte Carlo simulations, with implications for physical systems.

Contribution

It reveals a new condensation mechanism in non-heavy-tailed distributions conditioned on linear statistics, expanding understanding beyond traditional heavy-tailed cases.

Findings

Condensation occurs in non-heavy-tailed distributions under large deviation conditioning.

Monte Carlo simulations support the theoretical analysis.

The phenomenon applies to various physical systems.

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.