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

@article{Spohn2006ExactSF, title={Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals}, author={Herbert Spohn}, journal={Physica A-statistical Mechanics and Its Applications}, year={2006}, volume={369}, pages={71-99} }

## 78 Citations

From interacting particle systems to random matrices

- Mathematics
- 2010

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…

A combinatorial identity for the speed of growth in an anisotropic KPZ model

- Mathematics
- 2015

The speed of growth for a particular stochastic growth model introduced by Borodin and Ferrari in [Comm. Math. Phys. 325 (2014), 603-684], which belongs to the KPZ anisotropic universality class, was…

Extreme value problems in random matrix theory and other disordered systems

- Mathematics
- 2007

We review some applications of central limit theorems and extreme values statistics in the context of disordered systems. We discuss several problems, in particular concerning random matrix theory…

From interacting particle systems to random matrices Contribution to StatPhys 24 special issue

- Mathematics
- 2010

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 Kardar-Parisi-Zhang equation - a statistical physics perspective

- Physics
- 2018

The article covers the one-dimensional Kardar-Parisi-Zhang equation, weak drive limit, universality, directed polymers in a random medium, replica solutions, statistical mechanics of line ensembles,…

Symmetrized Models of Last Passage Percolation and Non-Intersecting Lattice Paths

- Mathematics, Computer Science
- 2007

A theory of the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups U(l), Sp(2l) and O(l) based on non-intersecting lattice paths, and integration techniques familiar from the theory ofrandom matrices.

Brownian Bridges for Late Time Asymptotics of KPZ Fluctuations in Finite Volume

- MathematicsJournal of Statistical Physics
- 2018

Height fluctuations are studied in the one-dimensional totally asymmetric simple exclusion process with periodic boundaries, with a focus on how late time relaxation towards the non-equilibrium…

Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques

- Chemistry
- 2007

The studies of fluctuations of the one-dimensional Kardar–Parisi–Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple…

Fluctuation Properties of the TASEP with Periodic Initial Configuration

- Mathematics
- 2007

Abstract
We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a…

The Kardar-Parisi-Zhang equation and universality class

- Mathematics
- 2011

Brownian motion is a continuum scaling limit for a wide class of random processes, and there has been great success in developing a theory for its properties (such as distribution functions or…

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