The KPZ equation on the real line

Perkowski, Nicolas; Rosati, Tommaso Cornelis

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The KPZ equation on the real line

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Author(s):	Perkowski, Nicolas ^[1] ; Rosati, Tommaso Cornelis ^[2] Total Authors: 2
Affiliation:	^[1] Free Univ Berlin, FB Math & Informat, Berlin - Germany ^[2] Humboldt Univ, Inst Math, Berlin - Germany Total Affiliations: 2
Document type:	Journal article
Source:	ELECTRONIC JOURNAL OF PROBABILITY; v. 24, 2019.
Web of Science Citations:	1
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. (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

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