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

Chin Hang Lun; Jon Warren

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arXiv · 1506.09030

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

Chin Hang Lun·Jon Warren

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Abstract

We prove the continuity and strict positivity of the multi-layer extension to the stochastic heat equation introduced in [OW11] 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.

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Chin Hang Lun, Jon Warren. 2015-06-30. Continuity and strict positivity of the multi-layer extension of the stochastic heat equation. https://arxiv.org/abs/1506.09030

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