Synchronization for KPZ

Author(s)

Rosati, Tommaso C.

• Document type: Journal article
• Source: Stochastics and Dynamics; v. 22, n. 04, p. 46-pg., 2022-06-01.

Abstract

We study the long-time behavior of Kardar-Parisi-Zhang (KPZ)-like equations: partial derivative(t)h(t, x) = Delta(x) h(t, x) + vertical bar del(x)h(t, x)vertical bar(2) + eta(t, x), h(0, x) = h(0)(x), (t, x) is an element of (0, infinity) x T-d, on the d-dimensional torus T-d driven by an ergodic noise eta (e.g., space-time white in d = 1). 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 Holder spaces. (AU)

• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants