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Anisotropic Growth of Random Surfaces in 2 + 1 Dimensions

- A. Borodin, P. Ferrari
- Mathematics
- 18 April 2008

We construct a family of stochastic growth models in 2 + 1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1 + 1 dimensional growth models in the… Expand

Fluctuation Properties of the TASEP with Periodic Initial Configuration

- A. Borodin, P. Ferrari, M. Praehofer, T. Sasamoto
- Mathematics
- 25 August 2006

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… Expand

Tracy–Widom asymptotics for $q$-TASEP

- P. Ferrari, Bálint Vető
- Mathematics
- 9 October 2013

We consider the q-TASEP that is a q-deformation of the totally asymmetric simple exclusion process (TASEP) on Z for q in [0,1) where the jump rates depend on the gap to the next particle. For step… Expand

Scaling Limit for the Space-Time Covariance of the Stationary Totally Asymmetric Simple Exclusion Process

- P. Ferrari, H. Spohn
- Mathematics
- 13 April 2005

The totally asymmetric simple exclusion process (TASEP) on the one-dimensional lattice with the Bernoulli ρ measure as initial conditions, 0<ρ<1, is stationary in space and time. Let Nt(j) be the… Expand

Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension

- A. Borodin, Ivan Corwin, P. Ferrari
- Mathematics
- 4 April 2012

We consider two models for directed polymers in space‐time independent random media (the O'Connell‐Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature… Expand

Constrained Brownian motion: Fluctuations away from circular and parabolic barriers

- P. Ferrari, H. Spohn
- Mathematics
- 26 August 2003

Motivated by the polynuclear growth model, we consider a Brownian bridge b(t) with b(±T) = 0 conditioned to stay above the semicircle cT(t) = p T 2 t2. In the limit of large T, the fluctuation scale… Expand

LETTER TO THE EDITOR: A determinantal formula for the GOE Tracy Widom distribution

- P. Ferrari, H. Spohn
- Business
- 4 May 2005

An apparatus and methods of making an electronic assembly. The electronic assembly comprises a functional block having at least one asymmetric feature. The functional block comprises an integrated… Expand

Fluctuations in the Discrete TASEP with Periodic Initial Configurations and the Airy1 Process

- A. Borodin, P. Ferrari, Michael Prahofer Caltech, TU-Muenchen
- Mathematics
- 26 November 2006

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 expressed as a Fredholm… Expand

Brownian motions with one-sided collisions: the stationary case

- P. Ferrari, H. Spohn, T. Weiss
- Mathematics
- 5 February 2015

AbstractWe consider an inﬁnite system of Brownian motions which interactthrough a given Brownian motion being reﬂected from its left neigh-bor. Earlier we studied this system for deterministic… Expand

Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure

- A. Borodin, P. Ferrari
- Mathematics
- 5 November 2008

In Borodin and Ferrari (2008 arXiv:0804.3035) we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in… Expand

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