Related papers: Constraint driven condensation in large fluctuatio…
An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…
We consider stochastic rules of mass transport which lead to steady states that factorize over the links of a one-dimensional ring. Based on the knowledge of the steady states, we derive the onset of a phase transition from a liquid to a…
We study condensation in several particle systems related to the inclusion process. For an asymmetric one-dimensional version with closed boundary conditions and drift to the right, we show that all but a finite number of particles condense…
The phenomenon of real-space condensation is encountered in a variety of situations such as aggregation and fragmentation processes, granular clustering, phase separation, traffic and networks. Unlike traditional Bose-Einstein condensation…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of…
The grand canonical thermodynamics of a bosonic system is studied in order to identify the footprint of its own high-density quantum phase transition. The phases displayed by the system at zero temperature establish recognizable patterns at…
We introduce a model of a preferential attachment based random graph which extends the family of models in which condensation phenomena can occur. Each vertex has an associated uniform random variable which we call its location. Our model…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
Non-equilibrium real-space condensation is a phenomenon in which a finite fraction of some conserved quantity (mass, particles, etc.) becomes spatially localised. We review two popular stochastic models of hopping particles that lead to…
Every driver knows that severe weather conditions cause traffic congestions. In many cases there is no direct reason for the congestion, and people tend to attribute it to the slow driving mode. Our computational study shows that the slow…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
We study the phenomenon of real space condensation in the steady state of a class of mass transport models where the steady state factorises. The grand canonical ensemble may be used to derive the criterion for the occurrence of a…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
A condensation transition was predicted for growing technological networks evolving by preferential attachment and competing quality of their nodes, as described by the fitness model. When this condensation occurs a node acquires a finite…
Condensation is characterized with a single macroscopic condensate whose mass is proportional to a system size $N$. We demonstrate how important particle interactions are in condensation phenomena. We study a modified version of the…
Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…
We address the question of condensation and extremes for three classes of intimately related stochastic processes: (a) random allocation models and zero-range processes, (b) tied-down renewal processes, (c) free renewal processes. While for…
A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…
Phase transitions not allowed in equilibrium steady states may happen however at the fluctuating level. We observe for the first time this striking and general phenomenon measuring current fluctuations in an isolated diffusive system. While…