From interacting particle systems to random matrices

Abstract

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.

18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.2

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Cited by in corpus (35)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Exact Current Statistics of the ASEP with Open Boundaries
• The Physicist's Companion to Current Fluctuations: One-Dimensional Bulk-Driven Lattice Gases
• Stationary correlations for the 1D KPZ equation
• The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class
• Universality of slow decorrelation in KPZ growth
• Finite time corrections in KPZ growth models
• Some Exact Results for the Exclusion Process
• Current moments of 1D ASEP by duality
• Bethe Ansatz and Q-operator for the open ASEP
• Matrix Ansatz for the Fluctuations of the Current in the ASEP with Open Boundaries
• Time-time covariance for last passage percolation with generic initial profile
• Tracy-Widom asymptotics for q-TASEP
• Replica approach to the KPZ equation with half Brownian motion initial condition
• Half-space stationary Kardar-Parisi-Zhang equation
• Revisiting Directed Polymers with heavy-tailed disorder
• Stationary half-space last passage percolation
• Height fluctuations for the stationary KPZ equation
• Generalized disorder averages and current fluctuations in run and tumble particles
• The lower tail of the half-space KPZ equation
• Extrapolation methods and Bethe ansatz for the asymmetric exclusion process
• Tracy-Widom limit of q-Hahn TASEP
• Nonlocal Asymmetric exclusion process on a ring and conformal invariance
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• Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume
• Brownian Gibbs property for Airy line ensembles
• Why random matrices share universal processes with interacting particle systems?
• Exact Large Deviations of the Current in the Asymmetric Simple Exclusion Process with Open Boundaries
• On the exponent governing the correlation decay of the Airy${}_1$ process
• Edge Universality for Nonintersecting Brownian Bridges
• Universal scaling and criticality of extremes in random matrix theory
• On ASEP with Periodic Step Bernoulli Initial Condition
• Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems
• The half-space Airy stat process
• The second class particle in the half-line open TASEP