Structure of the condensed phase in the inclusion process

Abstract

We establish a complete picture of condensation in the inclusion process in the thermodynamic limit with vanishing diffusion, covering all scaling regimes of the diffusion parameter and including large deviation results for the maximum occupation number. We make use of size-biased sampling to study the structure of the condensed phase, which can extend over more than one lattice site and exhibit an interesting hierarchical structure characterized by the Poisson-Dirichlet distribution. While this approach is established in other areas including population genetics or random permutations, we show that it also provides a powerful tool to analyse homogeneous condensation in stochastic particle systems with stationary product distributions. We discuss the main mechanisms beyond inclusion processes that lead to the interesting structure of the condensed phase, and the connection to other generic particle systems. Our results are exact, and we present Monte-Carlo simulation data and recursive numerics for partition functions to illustrate the main points.

29 pages, 4 figures

References in corpus (36)

• The large deviation approach to statistical mechanics
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Phase Transitions in one-dimensional nonequilibrium systems
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Duality and hidden symmetries in interacting particle systems
• Condensation in the zero range process: stationary and dynamical properties
• Duality and exact correlations for a model of heat conduction
• Duality for stochastic models of transport
• Interaction driven real-space condensation
• Exact Phase Diagram of a model with Aggregation and Chipping
• Condensation in the inclusion process and related models
• A simple stochastic model for the dynamics of condensation
• Condensation and Extreme Value Statistics
• Thermodynamic Limit for the Invariant Measures in Supercritical Zero Range Processes
• Conditional Distribution of Heavy Tailed Random Variables on Large Deviations of their Sum
• Spatial random permutations and Poisson-Dirichlet law of cycle lengths
• Condensation in stochastic particle systems with stationary product measures
• Zero Range Condensation at Criticality
• Condensation in stochastic mass transport models: beyond the zero-range process
• Explosive condensation in a mass transport model
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Discontinuous condensation transition and nonequivalence of ensembles in a zero-range process
• Finite size effects and metastability in zero-range condensation
• Zero-Range Processes with Multiple Condensates: Statics and Dynamics
• Lattice permutations and Poisson-Dirichlet distribution of cycle lengths
• Dynamics of condensation in the totally asymmetric inclusion process
• Instability of condensation in the zero-range process with random interaction
• Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion
• Condensation for random variables conditioned by the value of their sum
• Pair-factorized steady states on arbitrary graphs
• Coarsening dynamics in condensing zero-range processes and size-biased birth death chains
• Explosive condensation in symmetric mass transport models
• Monotonicity and Condensation in Homogeneous Stochastic Particle Systems
• A dynamical transition and metastability in a size-dependent zero-range process
• Condensation in randomly perturbed zero-range processes
• Emergence of particle clusters in a one-dimensional model: connection to condensation processes

Cited by in corpus (10)

• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Condensation and Metastable Behavior of Non-reversible Inclusion Processes
• Self-similar behavior of the exchange-driven growth model with product kernel
• On Random Allocation Models in the Thermodynamic Limit
• Size-biased diffusion limits and the inclusion process
• Poisson-Dirichlet asymptotics in condensing particle systems
• Partition function zeros of zeta-urns
• Spectral gap of the symmetric inclusion process
• Yang-Lee zeros for real-space condensation
• Condensation in zero-range processes with a fast rate