Local Brownian property of the narrow wedge solution of the KPZ equation

DOI10.1214/ECP.v16-1678zbMath1243.60054arXiv1105.0952OpenAlexW1967981968MaRDI QIDQ428707

Jeremy Quastel, Daniel Remenik

Publication date: 22 June 2012

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0952

zbMATH Keywords

Brownian motionasymmetric exclusion processstochastic heat equationdirected polymersfinite variationstochastic Burgers equationKardar-Parisi-Zhang equationrandom growth

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items (7)

KPZ line ensemble ⋮ Airy Processes and Variational Problems ⋮ Local behavior and hitting probabilities of the \(\text{Airy}_1\) process ⋮ A stochastic Burgers equation from a class of microscopic interactions ⋮ The KPZ equation with flat initial condition and the directed polymer with one free end ⋮ Brownian absolute continuity of the KPZ fixed point with arbitrary initial condition ⋮ Analysis of the gradient of the solution to a stochastic heat equation via fractional Brownian motion

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