Weak coupling limit of KPZ with rougher than white noise

Gerencsér, Máté; Toninelli, Fabio Lucio

doi:10.1214/25-ECP675

Record link:

http://hdl.handle.net/20.500.12708/215345

Title:

Weak coupling limit of KPZ with rougher than white noise

Citation:

Gerencsér, M., & Toninelli, F. L. (2025). Weak coupling limit of KPZ with rougher than white noise. Electronic Communications in Probability, 30, Article 34. https://doi.org/10.1214/25-ECP675

Publisher DOI:

10.1214/25-ECP675

CatalogPlus:

AC17518315

Publication Type:

Article - Original Research Article

Language:

English

Authors:

Gerencsér, Máté
Toninelli, Fabio Lucio

Organisational Unit:

E105-07 - Forschungsbereich Wahrscheinlichkeitstheorie
E101-01-4 - Forschungsgruppe Stochastische Differentialgleichungen

Journal:

Electronic Communications in Probability

ISSN:

1083-589X

Date (published):

2025

Number of Pages:

Publisher:

Institute of Mathematical Statistics (IMS)

Peer reviewed:

Yes

Keywords:

KPZ equation; weak coupling; regularity structures; stochastic partial differential equations

Abstract:

We consider the KPZ equation in 1 spatial dimension with noise that is rougher than white by an exponent γ > 1/4. Under a weak coupling limit, formally removing the nonlinearity from the equation, we show using regularity structures that the renormalised solutions converge to a Gaussian limit that is different from the solution of the linear part of the equation. The regime of this effect has a nontrivial overlap with the subcritical regime γ < 1/2.

Project title:

Stochastische PDEs und Renormierung: 101117125 (European Commission)
Stochastische Oberflächen: Wachstum und Universalität: P 35428-N (FWF - Österr. Wissenschaftsfonds)

Research Areas:

Fundamental Mathematics Research: 100%

Science Branch:

1020 - Informatik: 10%
5020 - Wirtschaftswissenschaften: 20%
1010 - Mathematik: 70%

License:

CC BY 4.0