Translator Disclaimer
2019 The KPZ equation on the real line
Nicolas Perkowski, Tommaso Cornelis Rosati
Electron. J. Probab. 24: 1-56 (2019). DOI: 10.1214/19-EJP362

Abstract

We prove existence and uniqueness of distributional solutions to the KPZ equation globally in space and time, with techniques from paracontrolled analysis. Our main tool for extending the analysis on the torus to the full space is a comparison result that gives quantitative upper and lower bounds for the solution. We then extend our analysis to provide a path-by-path construction of the random directed polymer measure on the real line and we derive a variational characterisation of the solution to the KPZ equation.

Citation

Download Citation

Nicolas Perkowski. Tommaso Cornelis Rosati. "The KPZ equation on the real line." Electron. J. Probab. 24 1 - 56, 2019. https://doi.org/10.1214/19-EJP362

Information

Received: 18 February 2019; Accepted: 8 September 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07142911
MathSciNet: MR4029420
Digital Object Identifier: 10.1214/19-EJP362

Subjects:
Primary: 35R60, 60H15

JOURNAL ARTICLE
56 PAGES


SHARE
Vol.24 • 2019
Back to Top