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.
First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
我们考虑一个单一的运行和翻滚粒子（RTP）在一维运动。我们假设粒子的速度是独立绘制在每个翻滚从零均值高斯分布和运行时间是指数分布。利用$N\gg 1$研究了粒子在$N$运行后的位置$X$的概率分布$P(X,N)$。我们表明，在政权$ X \sim N^{3/4}$的分布$P(X,N)$具有大的偏差形式，其特征在于由一个不连续的衍生物在临界值$X=X_c>0$的速率函数。由于$P(X,N)$的对称性，$X=-X_c$也是如此。我们发现，这种奇异性对应于一阶凝聚过渡：对于$X>X_c$一个单一的大跳跃占主导地位的RTP轨迹。我们考虑的参与率的单次运行的位移作为系统的序参量，表明这个量是不连续的$X=X_c$。我们的研究结果支持与约束马尔可夫链蒙特卡罗算法进行数值模拟。
The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: large deviations
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础科学研究所国际理论科学中心）；LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学法国国家科学研究中心理论与物质物理实验室）；Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589（索邦大学法国国家科学研究中心高能理论与物理实验室）
