Energy solutions of KPZ are unique
M Gubinelli, N Perkowski - Journal of the American Mathematical Society, 2018 - ams.org
The Kardar–Parisi–Zhang (KPZ) equation is conjectured to universally describe the
fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well …
fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well …
converges to the KPZ equation
I Corwin, H Shen, LC Tsai - 2018 - projecteuclid.org
ASEP(q,j) converges to the KPZ equation Page 1 www.imstat.org/aihp Annales de l’Institut
Henri Poincaré - Probabilités et Statistiques 2018, Vol. 54, No. 2, 995–1012 https://doi.org/10.1214/17-AIHP829 …
Henri Poincaré - Probabilités et Statistiques 2018, Vol. 54, No. 2, 995–1012 https://doi.org/10.1214/17-AIHP829 …
The Kardar–Parisi–Zhang equation as scaling limit of weakly asymmetric interacting Brownian motions
J Diehl, M Gubinelli, N Perkowski - Communications in Mathematical …, 2017 - Springer
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 that the large scale …
of a one-dimensional interface between two bulk phases. We prove that the large scale …
Non-equilibrium fluctuations of interacting particle systems
M Jara, O Menezes - arXiv preprint arXiv:1810.09526, 2018 - arxiv.org
We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density
of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is …
of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is …
From ABC to KPZ
G Cannizzaro, P Gonçalves, R Misturini… - arXiv preprint arXiv …, 2023 - arxiv.org
We study the equilibrium fluctuations of an interacting particle system evolving on the
discrete ring with three species of particles that we name $ A, B $ and $ C $, but at each site …
discrete ring with three species of particles that we name $ A, B $ and $ C $, but at each site …
Derivation of anomalous behavior from interacting oscillators in the high-temperature regime
P Gonçalves, K Hayashi - Communications in Mathematical Physics, 2023 - Springer
A microscopic model of interacting oscillators, which admits two conserved quantities,
volume, and energy, is investigated. We begin with a system driven by a general nonlinear …
volume, and energy, is investigated. We begin with a system driven by a general nonlinear …
KPZ fluctuations in finite volume
S Prolhac - SciPost Physics Lecture Notes, 2024 - scipost.org
These lecture notes, adapted from the habilitation thesis of the author, survey in a first part
various exact results obtained in the past few decades about KPZ fluctuations in one …
various exact results obtained in the past few decades about KPZ fluctuations in one …
Derivation of the stochastic Burgers equation with Dirichlet boundary conditions from the WASEP
P Gonçalves, N Perkowski… - Annales Henri …, 2020 - ahl.centre-mersenne.org
We consider the weakly asymmetric simple exclusion process on the discrete space {1,⋯, n-
1}(n∈ ℕ), in contact with stochastic reservoirs, both with density ρ∈(0, 1) at the extremity …
1}(n∈ ℕ), in contact with stochastic reservoirs, both with density ρ∈(0, 1) at the extremity …
Weakly asymmetric facilitated exclusion process
G Barraquand, O Blondel, M Simon - arXiv preprint arXiv:2301.04689, 2023 - arxiv.org
We consider the facilitated exclusion process, an interacting particle system on the integer
line where particles hop to one of their left or right neighbouring site only when the other …
line where particles hop to one of their left or right neighbouring site only when the other …
[HTML][HTML] Stochastic Burgers equation from long range exclusion interactions
P Gonçalves, M Jara - Stochastic Processes and their Applications, 2017 - Elsevier
We consider one-dimensional exclusion processes with long jumps given by a transition
probability of the form pn (⋅)= s (⋅)+ γ na (⋅), such that its symmetric part s (⋅) is irreducible …
probability of the form pn (⋅)= s (⋅)+ γ na (⋅), such that its symmetric part s (⋅) is irreducible …