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 …

These notes are based on lectures delivered by the authors at a Langeoog seminar of
SFB/TR12 Symmetries and Universality in Mesoscopic Systems to a mixed audience of …

The theory of random matrices plays an important role in many areas of pure mathematics
and employs a variety of sophisticated mathematical tools (analytical, probabilistic and …

We consider the solution of the stochastic heat equation\cal Z= 1 2\partial_X^ 2\cal Z-\cal Z ̇
W with delta function initial condition\cal Z (T= 0, X)= X= 0 whose logarithm, with appropriate …

Macdonald processes are probability measures on sequences of partitions defined in terms
of nonnegative specializations of the Macdonald symmetric functions and two Macdonald …

These lecture notes give a short review of methods such as the matrix ansatz, the additivity
principle or the macroscopic fluctuation theory, developed recently in the theory of non …

The One-Dimensional KPZ Equation and Its Universality Class | Journal of Statistical Physics
Skip to main content Springer Nature Link Account Menu Find a journal Publish with us Track …

We report on the first exact solution of the Kardar-Parisi-Zhang (KPZ) equation in one
dimension, with an initial condition which physically corresponds to the motion of a …

Abstract The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-
equilibrium fluctuations, including those of growing interfaces, directed polymers and …

The stochastic partial differential equation proposed nearly three decades ago by Kardar,
Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here …