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The Airy_1 process is not the limit of the largest eigenvalue in GOE matrix diffusion
Folkmar Bornemann, Patrik L. Ferrari, Michael Prähofer
Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy_1-process, arising as a limit law in stochastic surface grow…
Fluctuations in the discrete TASEP with periodic initial configurations and the Airy_1 process
Alexei Borodin, Patrik L. Ferrari, Michael Prähofer
We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with sequential update. The joint distribution of the positions of selected particles is expres…
Fluctuation properties of the TASEP with periodic initial configuration
Alexei Borodin, Patrik L. Ferrari, Michael Prähofer +1
We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants w…
One-dimensional stochastic growth and Gaussian ensembles of random matrices
Patrik L. Ferrari, Michael Praehofer
In this review paper we consider the polynuclear growth (PNG) model in one spatial dimension and its relation to random matrix ensembles. For curved and flat growth the scaling fun…
Stochastic Growth in One Dimension and Gaussian Multi-Matrix Models
Patrik L. Ferrari, Michael Praehofer, Herbert Spohn
We discuss the space-time determinantal random field which arises for the PNG model in one dimension and resembles the one for Dyson's Brownian motion. The information of interest…