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

2015/06/30 by Chin Hang Lun, Lun, Chin Hang, Jon Warren +1 · 1 citation
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1506.09030

openalex publication_date 2015/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the continuity and strict positivity of the multi-layer extension to\nthe stochastic heat equation introduced in [OW11] which form a hierarchy of\npartition functions for the continuum directed random polymer. This shows that\nthe corresponding free energy (logarithm of the partition function) is well\ndefined. This is also a step towards proving the conjecture stated at the end\nof the above paper that an array of such partition functions has the Markov\nproperty.\n

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