We consider the KPZ equation in space dimension 2 driven by spacetime white noise. We showed in previous work that if the noise is mollified in space on scale ε and its strength is scaled as β/√|log ε|, then a transition occurs with explicit critical point βc =√2π. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as ε ↓ 0, for sufficiently small β. We prove here that the limit exists in the entire subcritical regime β ∈ (0,βc) and we identify it as the solution of an additive stochastic heat equation, establishing so-called Edwards-Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension 2.

Caravenna, F., Sun, R., Zygouras, N. (2020). The two-dimensional KPZ equation in the entire subcritical regime. ANNALS OF PROBABILITY, 48(3), 1086-1127 [10.1214/19-AOP1383].

The two-dimensional KPZ equation in the entire subcritical regime

Caravenna F.;
2020

Abstract

We consider the KPZ equation in space dimension 2 driven by spacetime white noise. We showed in previous work that if the noise is mollified in space on scale ε and its strength is scaled as β/√|log ε|, then a transition occurs with explicit critical point βc =√2π. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as ε ↓ 0, for sufficiently small β. We prove here that the limit exists in the entire subcritical regime β ∈ (0,βc) and we identify it as the solution of an additive stochastic heat equation, establishing so-called Edwards-Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension 2.
Articolo in rivista - Articolo scientifico
Continuum limit; Directed polymer model; Edwards-wilkinson fluctuations; KPZ equation; Renormalization; Stochastic heat equation; White noise
English
1086
1127
42
Caravenna, F., Sun, R., Zygouras, N. (2020). The two-dimensional KPZ equation in the entire subcritical regime. ANNALS OF PROBABILITY, 48(3), 1086-1127 [10.1214/19-AOP1383].
Caravenna, F; Sun, R; Zygouras, N
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/284961
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