Communications in Mathematical Physics, ISSN 0010-3616, 1/2016, Volume 341, Issue 1, pp. 219 - 261

We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing the discrete Cole–Hopf transformation of Gärtner...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | RANDOM-MEDIA | ASEP | KPZ EQUATION | DIMENSION | FLUCTUATIONS | INTERFACES | DIRECTED POLYMERS | STOCHASTIC BURGERS | INITIAL CONDITION | PHYSICS, MATHEMATICAL | FREE-ENERGY

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | RANDOM-MEDIA | ASEP | KPZ EQUATION | DIMENSION | FLUCTUATIONS | INTERFACES | DIRECTED POLYMERS | STOCHASTIC BURGERS | INITIAL CONDITION | PHYSICS, MATHEMATICAL | FREE-ENERGY

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 2/2017, Volume 166, Issue 3, pp. 876 - 902

We use Renormalization Group to prove local well posedness for a generalized KPZ equation introduced by H. Spohn in the context of stochastic hydrodynamics....

Physical Chemistry | Theoretical, Mathematical and Computational Physics | KPZ equation | Quantum Physics | Physics | Stochastic hydrodynamics | Statistical Physics and Dynamical Systems | Renormalization group | PHYSICS, MATHEMATICAL

Physical Chemistry | Theoretical, Mathematical and Computational Physics | KPZ equation | Quantum Physics | Physics | Stochastic hydrodynamics | Statistical Physics and Dynamical Systems | Renormalization group | PHYSICS, MATHEMATICAL

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 3/2013, Volume 150, Issue 5, pp. 908 - 939

We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ...

Physical Chemistry | Theoretical, Mathematical and Computational Physics | KPZ equation | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Replica method | Physics | Exact solution | Fredholm determinant | DIRECTED POLYMERS | SIMPLE EXCLUSION PROCESS | PHYSICS, MATHEMATICAL | EXTERNAL SOURCES | RANDOM MATRICES | GROWING INTERFACES | POLYNUCLEAR GROWTH-MODEL | UNIVERSAL FLUCTUATIONS | INITIAL CONDITION | 1+1 DIMENSIONS | SCALING FUNCTIONS

Physical Chemistry | Theoretical, Mathematical and Computational Physics | KPZ equation | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Replica method | Physics | Exact solution | Fredholm determinant | DIRECTED POLYMERS | SIMPLE EXCLUSION PROCESS | PHYSICS, MATHEMATICAL | EXTERNAL SOURCES | RANDOM MATRICES | GROWING INTERFACES | POLYNUCLEAR GROWTH-MODEL | UNIVERSAL FLUCTUATIONS | INITIAL CONDITION | 1+1 DIMENSIONS | SCALING FUNCTIONS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 09/2017, Volume 354, Issue 2, pp. 549 - 589

We consider a system of infinitely many interacting Brownian motions that models the height of a one-dimensional interface between two bulk phases. We prove...

STOCHASTIC BURGERS-EQUATION | LANDAU LATTICE MODEL | KPZ EQUATION | PHI INTERFACE MODEL | PARTICLE-SYSTEMS | EQUILIBRIUM FLUCTUATIONS | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS | UNIVERSALITY CLASS | Energy industry | Analysis

STOCHASTIC BURGERS-EQUATION | LANDAU LATTICE MODEL | KPZ EQUATION | PHI INTERFACE MODEL | PARTICLE-SYSTEMS | EQUILIBRIUM FLUCTUATIONS | PHYSICS, MATHEMATICAL | LARGE DEVIATIONS | UNIVERSALITY CLASS | Energy industry | Analysis

Journal Article

Physical Review Letters, ISSN 0031-9007, 05/2012, Volume 108, Issue 19, p. 190603

We obtain the first exact solution for the stationary one-dimensional Kardar-Parisi-Zhang equation. A formula for the distribution of the height is given in...

GROWING INTERFACES | DISTRIBUTIONS | KPZ | PHYSICS, MULTIDISCIPLINARY | INITIAL CONDITION | SIMPLE EXCLUSION PROCESS | FREE-ENERGY | 1+1 DIMENSIONS | SCALING FUNCTIONS | RANDOM MATRICES | BETHE-ANSATZ

GROWING INTERFACES | DISTRIBUTIONS | KPZ | PHYSICS, MULTIDISCIPLINARY | INITIAL CONDITION | SIMPLE EXCLUSION PROCESS | FREE-ENERGY | 1+1 DIMENSIONS | SCALING FUNCTIONS | RANDOM MATRICES | BETHE-ANSATZ

Journal Article

Physical Review Letters, ISSN 0031-9007, 04/2010, Volume 104, Issue 15, p. 150601

We present a simple approximation of the nonperturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the...

DYNAMIC EXPONENT | KPZ EQUATION | PHYSICS, MULTIDISCIPLINARY | UPPER CRITICAL DIMENSION | DEPOSITION | EXPANSION | INTERFACES | GROWTH DYNAMICS

DYNAMIC EXPONENT | KPZ EQUATION | PHYSICS, MULTIDISCIPLINARY | UPPER CRITICAL DIMENSION | DEPOSITION | EXPANSION | INTERFACES | GROWTH DYNAMICS

Journal Article

Physical Review Letters, ISSN 0031-9007, 06/2011, Volume 106, Issue 25, p. 250603

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...

SCALE-INVARIANCE | GROUND-STATE | KPZ | PHYSICS, MULTIDISCIPLINARY | POLYNUCLEAR GROWTH | DIRECTED POLYMERS | SIMPLE EXCLUSION PROCESS | PROBABILITY-DISTRIBUTION | FREE-ENERGY | 1+1 DIMENSIONS | RANDOM MATRICES

SCALE-INVARIANCE | GROUND-STATE | KPZ | PHYSICS, MULTIDISCIPLINARY | POLYNUCLEAR GROWTH | DIRECTED POLYMERS | SIMPLE EXCLUSION PROCESS | PROBABILITY-DISTRIBUTION | FREE-ENERGY | 1+1 DIMENSIONS | RANDOM MATRICES

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 03/2012, Volume 85, Issue 3, p. 030102

We study aging during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems...

GROWING INTERFACES | SCALE-INVARIANCE | CONFORMAL FIELD-THEORY | KPZ | PHYSICS, FLUIDS & PLASMAS | GROWTH-PROCESSES | DIRECTED POLYMERS | BURGERS-EQUATION | MODEL | PHYSICS, MATHEMATICAL | OPERATORS | CONTACT PROCESS | Models, Chemical | Nanoparticles - chemistry | Computer Simulation | Surface Properties | Nanoparticles - ultrastructure | Models, Molecular | Crystallization - methods

GROWING INTERFACES | SCALE-INVARIANCE | CONFORMAL FIELD-THEORY | KPZ | PHYSICS, FLUIDS & PLASMAS | GROWTH-PROCESSES | DIRECTED POLYMERS | BURGERS-EQUATION | MODEL | PHYSICS, MATHEMATICAL | OPERATORS | CONTACT PROCESS | Models, Chemical | Nanoparticles - chemistry | Computer Simulation | Surface Properties | Nanoparticles - ultrastructure | Models, Molecular | Crystallization - methods

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 04/2018, Volume 128, Issue 4, pp. 1238 - 1293

In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel (2015), which is suitable for studying invariant measures. They...

Paracontrolled calculus | Cole–Hopf solution | KPZ equation | Invariant measure | STATISTICS & PROBABILITY | Cole-Hopf solution

Paracontrolled calculus | Cole–Hopf solution | KPZ equation | Invariant measure | STATISTICS & PROBABILITY | Cole-Hopf solution

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2015, Volume 48, Issue 48, pp. 485205 - 19

We show how the derivation of the Derrida-Lebowitz-Speer-Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the...

nonlinear diffusion | TracyWidom distribution | KPZ universality | Derrida-Lebowitz-Speer-Spohn equation | EXISTENCE | LARGE TIME ASYMPTOTICS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | Tracy-Widom distribution | 4TH-ORDER | PHYSICS, MATHEMATICAL | Derivation | Mathematical models | Numerical analysis | Approximation | Mathematical analysis | Mathematics

nonlinear diffusion | TracyWidom distribution | KPZ universality | Derrida-Lebowitz-Speer-Spohn equation | EXISTENCE | LARGE TIME ASYMPTOTICS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | Tracy-Widom distribution | 4TH-ORDER | PHYSICS, MATHEMATICAL | Derivation | Mathematical models | Numerical analysis | Approximation | Mathematical analysis | Mathematics

Journal Article

Annals of Probability, ISSN 0091-1798, 2017, Volume 45, Issue 6, pp. 4167 - 4221

We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but...

Wiener chaos | KPZ equation | Central limit theorem | Cumulants | cumulants | central limit theorem | PARTICLE-SYSTEMS | STATISTICS & PROBABILITY | REGULARITY STRUCTURES | RENORMALIZATION

Wiener chaos | KPZ equation | Central limit theorem | Cumulants | cumulants | central limit theorem | PARTICLE-SYSTEMS | STATISTICS & PROBABILITY | REGULARITY STRUCTURES | RENORMALIZATION

Journal Article

Physical Review Letters, ISSN 0031-9007, 02/2016, Volume 116, Issue 7, p. 070601

Using the weak-noise theory, we evaluate the probability distribution P(H, t) of large deviations of height H of the evolving surface height h(x, t) in the...

GROWING INTERFACES | DISTRIBUTIONS | SCALE-INVARIANCE | KPZ EQUATION | PHYSICS, MULTIDISCIPLINARY | UNIVERSAL FLUCTUATIONS | GROWTH | TURBULENCE | Frames | Asymptotic properties | Mathematical analysis | Flats | Evolution | Gaussian | Deviation | Optimization | Physics - Statistical Mechanics

GROWING INTERFACES | DISTRIBUTIONS | SCALE-INVARIANCE | KPZ EQUATION | PHYSICS, MULTIDISCIPLINARY | UNIVERSAL FLUCTUATIONS | GROWTH | TURBULENCE | Frames | Asymptotic properties | Mathematical analysis | Flats | Evolution | Gaussian | Deviation | Optimization | Physics - Statistical Mechanics

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 10/2013, Volume 88, Issue 4, p. 042118

Following our numerical work [Phys. Rev. Lett. 109, 170602 (2012)] focused upon the 2 + 1 Kardar-Parisi-Zhang (KPZ) equation with flat initial condition, we...

RANDOM-MEDIA | DISTRIBUTIONS | KPZ EQUATION | PHYSICS, FLUIDS & PLASMAS | UPPER CRITICAL DIMENSION | GROWTH-PROCESSES | FLUCTUATIONS | INTERFACES | DIRECTED POLYMERS | PHYSICS, MATHEMATICAL | SCALING FUNCTIONS | RANDOM MATRICES

RANDOM-MEDIA | DISTRIBUTIONS | KPZ EQUATION | PHYSICS, FLUIDS & PLASMAS | UPPER CRITICAL DIMENSION | GROWTH-PROCESSES | FLUCTUATIONS | INTERFACES | DIRECTED POLYMERS | PHYSICS, MATHEMATICAL | SCALING FUNCTIONS | RANDOM MATRICES

Journal Article

ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2019, Volume 24

We prove existence and uniqueness of distributional solutions to the KPZ equation globally in space and time, with techniques from paracontrolled analysis. Our...

INTEGRALS | CONSTRUCTION | KPZ equation | STOCHASTIC BURGERS | STATISTICS & PROBABILITY | NOISE | MODEL | singular SPDEs | paracontrolled distributions | comparison principle

INTEGRALS | CONSTRUCTION | KPZ equation | STOCHASTIC BURGERS | STATISTICS & PROBABILITY | NOISE | MODEL | singular SPDEs | paracontrolled distributions | comparison principle

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 11/2012, Volume 86, Issue 5, p. 051124

We investigate the strong-coupling regime of the stationary Kardar-Parisi-Zhang equation for interfaces growing on a substrate of dimension d = 1, 2, and 3...

GROWING INTERFACES | INVARIANCE | EXPONENTS | KPZ EQUATION | PHYSICS, FLUIDS & PLASMAS | NOISY BURGERS-EQUATION | UNIVERSAL FLUCTUATIONS | DYNAMICS | DIRECTED POLYMERS | SURFACE GROWTH | MODEL | PHYSICS, MATHEMATICAL | Algorithms | Models, Statistical | Stochastic Processes | Computer Simulation

GROWING INTERFACES | INVARIANCE | EXPONENTS | KPZ EQUATION | PHYSICS, FLUIDS & PLASMAS | NOISY BURGERS-EQUATION | UNIVERSAL FLUCTUATIONS | DYNAMICS | DIRECTED POLYMERS | SURFACE GROWTH | MODEL | PHYSICS, MATHEMATICAL | Algorithms | Models, Statistical | Stochastic Processes | Computer Simulation

Journal Article

STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, ISSN 2194-0401, 03/2020, Volume 8, Issue 1, pp. 150 - 185

We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards-Wilkinson equation...

UNIVERSALITY | MATHEMATICS, APPLIED | STOCHASTIC HEAT-EQUATION | Feynman-Kac formula | KPZ equation | STATISTICS & PROBABILITY | LIMIT | Edwards-Wilkinson equation

UNIVERSALITY | MATHEMATICS, APPLIED | STOCHASTIC HEAT-EQUATION | Feynman-Kac formula | KPZ equation | STATISTICS & PROBABILITY | LIMIT | Edwards-Wilkinson equation

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 1/2017, Volume 166, Issue 1, pp. 150 - 168

We consider the transition probabilities for random walks in $$1+1$$ 1 + 1 dimensional space-time random environments (RWRE). For critically tuned weak...

Random walk in random environment | Physical Chemistry | Theoretical, Mathematical and Computational Physics | KPZ equation | Quantum Physics | Sharp large deviation | Physics | Statistical Physics and Dynamical Systems | PHYSICS, MATHEMATICAL | DIMENSION | FREE-ENERGY

Random walk in random environment | Physical Chemistry | Theoretical, Mathematical and Computational Physics | KPZ equation | Quantum Physics | Sharp large deviation | Physics | Statistical Physics and Dynamical Systems | PHYSICS, MATHEMATICAL | DIMENSION | FREE-ENERGY

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 12/2017, Volume 127, Issue 12, pp. 4029 - 4052

We consider one-dimensional exclusion processes with long jumps given by a transition probability of the form pn(⋅)=s(⋅)+γna(⋅), such that its symmetric part...

KPZ equation | Stochastic Burgers equation | Long range exclusion | Universality | Equilibrium fluctuations | PARTICLE-SYSTEMS | STATISTICS & PROBABILITY

KPZ equation | Stochastic Burgers equation | Long range exclusion | Universality | Equilibrium fluctuations | PARTICLE-SYSTEMS | STATISTICS & PROBABILITY

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 2015, Volume 158, Issue 6, pp. 1262 - 1270

We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying...

KPZ equation | Gradient Kawasaki dynamics | Einstein relation | Equilibrium fluctuations | EXCLUSION PROCESSES | INTERACTING PARTICLE-SYSTEMS | FLUCTUATIONS | PHYSICS, MATHEMATICAL

KPZ equation | Gradient Kawasaki dynamics | Einstein relation | Equilibrium fluctuations | EXCLUSION PROCESSES | INTERACTING PARTICLE-SYSTEMS | FLUCTUATIONS | PHYSICS, MATHEMATICAL

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 12/2011, Volume 84, Issue 6, p. 061128

We present an analytical method, rooted in the nonperturbative renormalization group, that allows one to calculate the critical exponents and the correlation...

STATISTICAL-MECHANICS | DYNAMIC EXPONENT | KPZ EQUATION | CORRELATED NOISE | PHYSICS, FLUIDS & PLASMAS | UPPER CRITICAL DIMENSION | DIRECTED POLYMERS | BURGERS-EQUATION | PHYSICS, MATHEMATICAL | DRIVEN DIFFUSIVE SYSTEMS | SCALING FUNCTIONS | INTERFACE GROWTH | Condensed Matter | Physics | Statistical Mechanics

STATISTICAL-MECHANICS | DYNAMIC EXPONENT | KPZ EQUATION | CORRELATED NOISE | PHYSICS, FLUIDS & PLASMAS | UPPER CRITICAL DIMENSION | DIRECTED POLYMERS | BURGERS-EQUATION | PHYSICS, MATHEMATICAL | DRIVEN DIFFUSIVE SYSTEMS | SCALING FUNCTIONS | INTERFACE GROWTH | Condensed Matter | Physics | Statistical Mechanics

Journal Article

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