The directed landscape
The conjectured limit of last passage percolation is a scale-invariant, independent,
stationary increment process with respect to metric composition. We prove this for Brownian …
stationary increment process with respect to metric composition. We prove this for Brownian …
Fixed point theory: A review
arxiv:2309.03226v1 [math.HO] 3 Sep 2023 Page 1 arxiv:2309.03226v1 [math.HO] 3 Sep 2023
FIXED POINT THEORY: A REVIEW FIRUZ KAMALOV∗ AND HO HON LEUNG2 Abstract …
FIXED POINT THEORY: A REVIEW FIRUZ KAMALOV∗ AND HO HON LEUNG2 Abstract …
Convergence of exclusion processes and the KPZ equation to the KPZ fixed point
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) …
function of finite range asymmetric exclusion processes and the Kardar-Parisi-Zhang (KPZ) …
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 …
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 …
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 …
geometry described by the directed landscape. In this first part, we show that the O'Connell …
Stationary measures for integrable polymers on a strip
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 …
geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal …
Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a
century, the anomalous nature of its high-temperature transport dynamics has only recently …
century, the anomalous nature of its high-temperature transport dynamics has only recently …
The stationary horizon and semi-infinite geodesics in the directed landscape
The stationary horizon (SH) is a stochastic process of coupled Brownian motions indexed by
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …
their real-valued drifts. It was first introduced by the first author as the diffusive scaling limit of …
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 …
THE KPZ EQUATION AND THE DIRECTED LANDSCAPE XUAN WU Abstract. This paper …