Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals

Abstract

Three models from statistical physics can be analyzed by employing space-time determinantal processes: (1) crystal facets, in particular the statistical properties of the facet edge, and equivalently tilings of the plane, (2) one-dimensional growth processes in the Kardar-Parisi-Zhang universality class and directed last passage percolation, (3) random matrices, multi-matrix models, and Dyson's Brownian motion. We explain the method and survey results of physical interest.

Lecture Notes: Fundamental Problems in Statistical Mechanics XI, Leuven, September 4 - 16, 2005

References in corpus (9)

• Exact scaling functions for one-dimensional stationary KPZ growth
• The Pearcey Process
• Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Fluctuations of a one-dimensional polynuclear growth model in a half space
• A determinantal formula for the GOE Tracy-Widom distribution
• Domino tilings and the six-vertex model at its free fermion point
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• Step fluctuations for a faceted crystal

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• Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems
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• Nonintersecting random walks in the neighborhood of a symmetric tacnode
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• Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
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• Two speed TASEP
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• Free fermions at the edge of interacting systems
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
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• The universal Airy_1 and Airy_2 processes in the Totally Asymmetric Simple Exclusion Process
• Half-space stationary Kardar-Parisi-Zhang equation
• Kardar-Parisi-Zhang Universality of the Nagel-Schreckenberg Model
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• Spectrum of the totally asymmetric simple exclusion process on a periodic lattice -- first excited states
• Revisiting Directed Polymers with heavy-tailed disorder
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• Extreme boundary conditions and random tilings
• Memory effects in the Fermi-Pasta-Ulam Model
• Symmetrized models of last passage percolation and non-intersecting lattice paths
• Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation: numerical study
• Comment on "Dynamic Scaling of Non-Euclidean Interfaces" [arXiv:0804.1898]
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• KPZ fluctuations in finite volume
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• Slow melting of a disordered quantum crystal
• A combinatorial solution for the current fluctuations in the exclusion process
• Correlation function of the Schur process with a fixed final partition
• Approach to stationarity for the KPZ fixed point with boundaries
• Asymmetric simple exclusion process in one-dimensional chains with long-range links
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions
• Nonequilibrium phases and quantum correlations in synthetic transport models