Synchronization for KPZ

2021/11/03 by Tommaso Rosati · 1 voice
Mathematics · #Random Matrices and Applications #Spectral Theory in Mathematical Physics #Stochastic processes and statistical mechanics

paper · doi:10.1142/s0219493722500101

openalex publication_date 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the long-time behavior of Kardar–Parisi–Zhang (KPZ)-like equations: [Formula: see text] [Formula: see text] on the [Formula: see text]-dimensional torus [Formula: see text] driven by an ergodic noise [Formula: see text] (e.g., space-time white in [Formula: see text]). The analysis builds on infinite-dimensional extensions of similar results for positive random matrices. We establish a one force, one solution principle and derive almost sure synchronization with exponential deterministic speed in appropriate Hölder spaces.

Citations

• Random dynamical systems
• An analytic BPHZ theorem for regularity structures

Cited by

• Synchronisation by noise for the stochastic quantisation equation in dimensions 2 and 3
• Ergodicity for singular-degenerate porous media equations

Discussions

• How do KPZ-like equations behave over time when driven by random noise? Tommaso C. Rosati studies long-time behaviour in KPZ-type models, establishing a “one force, one solution” principle and almost [bsky, 0 points, 0 comments]