Real-space Condensation in Stochastic Mass Transport Models

Abstract

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 in the momentum space, a condensate in these systems forms in real space, e.g., upon increasing the density beyond a critical value a macroscopically large mass/cluster may form at a single site on a lattice. In this brief review, I discuss some recent developments in understanding the physical and mathematical mechanism behind this real-space condensation in a class of simple stochastic mass transport models.

Les Houches lecture notes for the summer school "Exact Methods in Low-dimensional Statistical Physics and Quantum Computing" (2008); 16 pages, 3 figures included

References in corpus (1)

• Evolution of networks

Cited by in corpus (8)

• Condensation transition in the late-time position of a Run-and-Tumble particle
• Extremal statistics for stochastic resetting systems
• Condensation transition in joint large deviations of linear statistics
• Motion of condensates in non-Markovian zero-range dynamics
• Participation ratio for constraint-driven condensation with superextensive mass
• Extreme eigenvalues and the emerging outlier in rank-one non-Hermitian deformations of the Gaussian Unitary Ensemble
• Emergent motion of condensates in mass-transport models
• Subleading-order theory for condensation transitions in large deviations of sums of independent and identically distributed random variables