Condensation in the inclusion process and related models

Abstract

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 on the right-most site. This is extended to a general result for independent random variables with different tails, where condensation occurs for the index (site) with the heaviest tail, generalizing also previous results for zero-range processes. For inclusion processes with homogeneous stationary measures we establish condensation in the limit of vanishing diffusion strength in the dynamics, and give several details about how the limit is approached for finite and infinite systems. Finally, we consider a continuous model dual to the inclusion process, the so-called Brownian energy process, and prove similar condensation results.

29 pages, 3 figures, to appear in J. Stat. Phys

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• Condensation transition in joint large deviations of linear statistics
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• The bosonic skin effect: boundary condensation in asymmetric transport
• Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process
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• Derivation of mean-field equations for stochastic particle systems
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• Explosive condensation in symmetric mass transport models
• Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with Open Boundaries
• Occupancy correlations in the asymmetric simple inclusion process
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Stationary distributions via decomposition of stochastic reaction networks
• Large deviations of density fluctuations in the boundary driven Quantum Symmetric Simple Inclusion Process
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• A Unified Interface Model for Dissipative Transport of Bosons and Fermions
• Size-biased diffusion limits and the inclusion process
• Condensation in models with factorized and pair-factorized stationary states
• Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies
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• Second Time Scale of the Metastability of Reversible Inclusion Processes
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• Quantitative results for the Fleming-Viot Particle system and quasi-stationary distributions in discrete space
• Spectral gap of the symmetric inclusion process
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