The Kardar–Parisi–Zhang equation and universality class
I Corwin - Random matrices: Theory and applications, 2012 - World Scientific
Brownian motion is a continuum scaling limit for a wide class of random processes, and
there has been great success in develo** a theory for its properties (such as distribution …
there has been great success in develo** a theory for its properties (such as distribution …
Growing interfaces uncover universal fluctuations behind scale invariance
Stochastic motion of a point–known as Brownian motion–has many successful applications
in science, thanks to its scale invariance and consequent universal features such as …
in science, thanks to its scale invariance and consequent universal features such as …
Anisotropic growth of random surfaces in 2+ 1 dimensions
A Borodin, PL Ferrari - Communications in Mathematical Physics, 2014 - Springer
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 …
anisotropic KPZ class. Appropriate projections of these models yield 1+ 1 dimensional …
Height fluctuations for the stationary KPZ equation
We compute the one-point probability distribution for the stationary KPZ equation (ie initial
data H (0, X)= B (X) H(0,X)=B(X), for B (X) a two-sided standard Brownian motion) and show …
data H (0, X)= B (X) H(0,X)=B(X), for B (X) a two-sided standard Brownian motion) and show …
Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in
liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar …
liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar …
Large time asymptotics of growth models on space-like paths I: PushASEP
A Borodin, P Ferrari - 2008 - projecteuclid.org
We consider a new interacting particle system on the one-dimensional lattice that
interpolates between TASEP and Toom's model: A particle cannot jump to the right if the …
interpolates between TASEP and Toom's model: A particle cannot jump to the right if the …
Temporal correlation in last passage percolation with flat initial condition via Brownian comparison
We consider directed last passage percolation on Z^ 2 Z 2 with exponential passage times
on the vertices. A topic of great interest is the coupling structure of the weights of geodesics …
on the vertices. A topic of great interest is the coupling structure of the weights of geodesics …
Hausdorff dimensions for shared endpoints of disjoint geodesics in the directed landscape
Abstract Within the Kardar–Parisi–Zhang universality class, the space-time Airy sheet is
conjectured to be the canonical scaling limit for last passage percolation models. In recent …
conjectured to be the canonical scaling limit for last passage percolation models. In recent …
Random growth models
The link between a particular class of growth processes and random matrices was
established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the …
established in the now famous 1999 article of Baik, Deift, and Johansson on the length of the …
Pfaffian Schur processes and last passage percolation in a half-quadrant
We study last passage percolation in a half-quadrant, which we analyze within the
framework of Pfaffian Schur processes. For the model with exponential weights, we prove …
framework of Pfaffian Schur processes. For the model with exponential weights, we prove …