The one-dimensional KPZ equation and its universality class

J Quastel, H Spohn - Journal of Statistical Physics, 2015 - Springer
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Convergence of exclusion processes and the KPZ equation to the KPZ fixed point

J Quastel, S Sarkar - Journal of the American Mathematical Society, 2023 - ams.org
We show that under the 1: 2: 3 scaling, critically probing large space and time, the height
function of finite range asymmetric exclusion processes and the Kardar-Parisi-Zhang (KPZ) …

Some recent progress on the stationary measure for the open KPZ equation

I Corwin - Toeplitz Operators and Random Matrices: In Memory of …, 2022 - Springer
This note is an expanded version of a lecture I gave in fall 2021 at the MSRI program
“Universality and Integrability in Random Matrices and Interacting Particle Systems”. I will …

The scaling limit of the longest increasing subsequence

D Dauvergne, B Virág - arXiv preprint arXiv:2104.08210, 2021 - arxiv.org
We provide a framework for proving convergence to the directed landscape, the central
object in the Kardar-Parisi-Zhang universality class. For last passage models, we show that …

The heat and the landscape I

B Virág - arXiv preprint arXiv:2008.07241, 2020 - arxiv.org
Heat flows in 1+ 1 dimensional stochastic environment converge after scaling to the random
geometry described by the directed landscape. In this first part, we show that the O'Connell …

Stationary measures for integrable polymers on a strip

G Barraquand, I Corwin, Z Yang - Inventiones mathematicae, 2024 - Springer
We prove that the stationary measures for the free-energy increment process for the
geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal …

The critical 2d stochastic heat flow

F Caravenna, R Sun, N Zygouras - Inventiones mathematicae, 2023 - Springer
We consider directed polymers in random environment in the critical dimension d= 2,
focusing on the intermediate disorder regime when the model undergoes a phase transition …

Height fluctuations for the stationary KPZ equation

A Borodin, I Corwin, P Ferrari, B Vető - Mathematical Physics, Analysis and …, 2015 - Springer
We compute the one-point probability distribution for the stationary KPZ equation (ie initial
data H (0, X)= B (X) H(0,X)=B(X), for B (X) a two-sided standard Brownian motion) and show …

The KPZ equation and the directed landscape

X Wu - arXiv preprint arXiv:2301.00547, 2023 - arxiv.org
arXiv:2301.00547v2 [math.PR] 4 Apr 2023 Page 1 arXiv:2301.00547v2 [math.PR] 4 Apr 2023
THE KPZ EQUATION AND THE DIRECTED LANDSCAPE XUAN WU Abstract. This paper …

Lower tail of the KPZ equation

I Corwin, P Ghosal - 2020 - projecteuclid.org
We provide the first tight bounds on the lower tail probability of the one-point distribution of
the Kardar–Parisi–Zhang (KPZ) equation with narrow wedge initial data. Our bounds hold …