Condensation and Extreme Value Statistics

Abstract

We study the factorised steady state of a general class of mass transport models in which mass, a conserved quantity, is transferred stochastically between sites. Condensation in such models is exhibited when above a critical mass density the marginal distribution for the mass at a single site develops a bump, $p_{\mathrm{cond}}(m)$, at large mass $m$. This bump corresponds to a condensate site carrying a finite fraction of the mass in the system. Here, we study the condensation transition from a different aspect, that of extreme value statistics. We consider the cumulative distribution of the largest mass in the system and compute its asymptotic behaviour. We show 3 distinct behaviours: at subcritical densities the distribution is Gumbel; at the critical density the distribution is Fréchet, and above the critical density a different distribution emerges. We relate $p_{\mathrm{cond}}(m)$ to the probability density of the largest mass in the system.

11 pages 2 figure

References in corpus (35)

• Evolution of networks
• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• A Model for Force Fluctuations in Bead Packs
• Phase Transitions in one-dimensional nonequilibrium systems
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
• Condensation in the zero range process: stationary and dynamical properties
• Exact Maximal Height Distribution of Fluctuating Interfaces
• Criterion for phase separation in one-dimensional driven systems
• Nonequilibrium Phase Transitions in Models of Aggregation, Adsorption, and Dissociation
• The Nature of the Condensate in Mass Transport Models
• Canonical Analysis of Condensation in Factorised Steady State
• Condensation in the Backgammon model
• On the top eigenvalue of heavy-tailed random matrices
• Factorised Steady States in Mass Transport Models
• Extreme Value Statistics of Hierarchically Correlated Variables: Deviation from Gumbel Statistics and Anomalous Persistence
• Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation and Fragmentation
• Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
• Zero range model of traffic flow
• Maximal height statistics for 1/f^alpha signals
• Extremal Paths on a Random Cayley Tree
• Statistics of extremal intensities for Gaussian interfaces
• Asymmetric particle systems on R
• Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
• Factorised Steady States in Mass Transport Models on an Arbitrary Graph
• Extreme statistics of complex random and quantum chaotic states
• Analytic study of clustering in shaken granular material using zero-range processes
• Condensation for a fixed number of independent random variables
• Critical phase in non-conserving zero-range processes and equilibrium networks
• Construction of the factorized steady state distribution in models of mass transport
• Condensation transitions in a model for a directed network with weighted links
• Broken Ergodicity in a Stochastic Model with Condensation
• An exactly solvable dissipative transport model

Cited by in corpus (36)

• Random Convex Hulls and Extreme Value Statistics
• Condensation transition in the late-time position of a Run-and-Tumble particle
• Extremal statistics for stochastic resetting systems
• Zero Range Condensation at Criticality
• Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
• Transport in disordered systems: the single big jump approach
• Exact extreme value statistics at mixed order transitions
• Finite size effects and metastability in zero-range condensation
• Extreme value statistics and arcsine laws for heterogeneous diffusion processes
• Anomalous scaling and first-order dynamical phase transition in large deviations of the Ornstein-Uhlenbeck process
• Extreme reductions of entropy in an electronic double dot
• On the concentration of large deviations for fat tailed distributions, with application to financial data
• Discrete Sampling of Extreme Events Modifies Their Statistics
• Large deviations, condensation, and giant response in a statistical system
• Condensation for random variables conditioned by the value of their sum
• Record statistics in random vectors and quantum chaos
• Real-Space Renormalization for disordered systems at the level of Large Deviations
• Extremal statistics of a one dimensional run and tumble particle with an absorbing wall
• Extreme-value statistics of networks with inhibitory and excitatory couplings
• Extreme value theory for constrained physical systems
• Development and regression of a large fluctuation
• Condensation and extremes for a fluctuating number of independent random variables
• Structure of the condensed phase in the inclusion process
• Analytical Study of Giant Fluctuations and Temporal Intermittency in an Aggregation Model
• Participation ratio for constraint-driven condensation with superextensive mass
• Two-point correlation function of an exclusion process with hole-dependent rates
• Quantum widening of CDT universe
• Particle Condensation in Pair Exclusion Process
• Interplay of inhibition and multiplexing : Largest eigenvalue statistics
• Coarsening, condensates and extremes in aggregation-fragmentation models
• Interaction-correlated random matrices
• Extreme value distributions for weakly correlated fitnesses in block model
• Finite-size effects in dynamics of zero-range processes
• Universality of Top Rank Statistics for Brownian Reshuffling
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Asymmetric scaling in large deviations for rare values bigger or smaller than the typical value