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Continuity and strict positivity of the multi-layer extension of the stochastic heat equation

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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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Official URL: https://doi.org/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:
DateEvent
2020Published
14 September 2020Available
10 August 2020Accepted
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 IDRIOXX Funder NameFunder ID
EP/H023364/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266

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