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 …

A pedestrian's view on interacting particle systems, KPZ universality and random matrices

T Kriecherbauer, J Krug - Journal of Physics A: Mathematical and …, 2010 - iopscience.iop.org
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 …

Nonlinear fluctuating hydrodynamics for anharmonic chains

H Spohn - Journal of Statistical Physics, 2014 - Springer
With focus on anharmonic chains, we develop a nonlinear version of fluctuating
hydrodynamics, in which the Euler currents are kept to second order in the deviations from …

An appetizer to modern developments on the Kardar–Parisi–Zhang universality class

KA Takeuchi - Physica A: Statistical Mechanics and its Applications, 2018 - Elsevier
Abstract The Kardar–Parisi–Zhang (KPZ) universality class describes a broad range of non-
equilibrium fluctuations, including those of growing interfaces, directed polymers and …

Growing interfaces uncover universal fluctuations behind scale invariance

KA Takeuchi, M Sano, T Sasamoto, H Spohn - Scientific reports, 2011 - nature.com
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 …

Free-energy distribution of the directed polymer at high temperature

P Calabrese, P Le Doussal, A Rosso - Europhysics Letters, 2010 - iopscience.iop.org
We study the directed polymer of length t in a random potential with fixed endpoints in
dimension 1+ 1 in the continuum and on the square lattice, by analytical and numerical …

[BOOK][B] Fluctuations in Markov processes: time symmetry and martingale approximation

T Komorowski, C Landim, S Olla - 2012 - books.google.com
The present volume contains the most advanced theories on the martingale approach to
central limit theorems. Using the time symmetry properties of the Markov processes, the …

The KPZ fixed point

K Matetski, J Quastel, D Remenik - Acta Mathematica, 2021 - projecteuclid.org
An explicit Fredholm determinant formula is derived for the multipoint distribution of the
height function of the totally asymmetric simple exclusion process (TASEP) with arbitrary …

[PDF][PDF] Introduction to KPZ

J Quastel - Current developments in mathematics, 2011 - math.toronto.edu
1. A physical introduction 2 1.1. KPZ/Stochastic Burgers/Scaling exponent 2 1.2. Physical
derivation 3 1.3. Scaling 3 1.4. Formal invariance of Brownian motion 4 1.5. Dynamic scaling …

Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions

P Calabrese, P Le Doussal - Physical review letters, 2011 - APS
We provide the first exact calculation of the height distribution at arbitrary time t of the
continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial …