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2020 Continuity and strict positivity of the multi-layer extension of the stochastic heat equation
Chin Hang Lun, Jon Warren
Electron. J. Probab. 25: 1-41 (2020). DOI: 10.1214/20-EJP511

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.

Citation

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Chin Hang Lun. Jon Warren. "Continuity and strict positivity of the multi-layer extension of the stochastic heat equation." Electron. J. Probab. 25 1 - 41, 2020. https://doi.org/10.1214/20-EJP511

Information

Received: 5 September 2019; Accepted: 10 August 2020; Published: 2020
First available in Project Euclid: 14 September 2020

zbMATH: 07252703
MathSciNet: MR4150521
Digital Object Identifier: 10.1214/20-EJP511

Subjects:
Primary: 60K35

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