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arXiv · 1907.06278

Synchronization for KPZ

Tommaso Cornelis Rosati
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Abstract

We study the longtime behavior of KPZ-like equations: $$ \partial_{t}h(t,x) = Δ_{x} h (t, x) + | \nabla_{x}h (t,x)|^{2} + η(t, x), \qquad h(0, x) = h_0(x), \qquad (t, x) \in (0, \infty) \times \mathbb{T}^{d} $$ on the $d-$dimensional torus $\mathbb{T}^{d}$ driven by an ergodic noise $η$ (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 Hölder spaces.

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Tommaso Cornelis Rosati. 2021-09-29. Synchronization for KPZ. https://arxiv.org/abs/1907.06278

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