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

Chin Hang Lun, Jon Warren

Published 2015-06-30Version 1

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.