Hang Lun, Chin and Warren, Jon (2020) Continuity and strict positivity of the multi-layer extension of the stochastic heat equation. Electronic Journal of Probability, 25 . 109. doi:10.1214/20-EJP511

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Abstract

We prove the continuity and strict positivity of the multi-layer extension to the stochastic heat equation introduced in [43] which form a hierarchy of partition functions for the continuum directed random polymer. This shows that the corresponding free energy (logarithm of the partition function) is well defined. This is also a step towards proving the conjecture stated at the end of the above paper that an array of such partition functions has the Markov property.

Item Type:	Journal Article
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics Q Science > QC Physics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Stochastic differential equations, Probability, Mathematical statistics
Journal or Publication Title:	Electronic Journal of Probability
Publisher:	University of Washington. Dept. of Mathematics
ISSN:	1083-6489
Official Date:	2020
Dates:	Date Event 2020 Published 14 September 2020 Available 10 August 2020 Accepted
Date of first compliant deposit:	22 September 2020
Volume:	25
Article Number:	109
DOI:	10.1214/20-EJP511
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID EP/H023364/1 [EPSRC] Engineering and Physical Sciences Research Council http://dx.doi.org/10.13039/501100000266

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