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 …
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 …
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 …
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 …
equilibrium fluctuations, including those of growing interfaces, directed polymers and …
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 …
Free-energy distribution of the directed polymer at high temperature
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 …
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
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 …
central limit theorems. Using the time symmetry properties of the Markov processes, the …
The KPZ fixed point
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 …
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 …
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
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 …
continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial …