Two time distribution in Brownian directed percolation

Abstract

In the zero temperature Brownian semi-discrete directed polymer we study the joint distribution of two last-passage times at positions ordered in the time-like direction. This is the situation when we have the slow de-correlation phenomenon. We compute the limiting joint distribution function in a scaling limit. This limiting distribution is given by an expansion in determinants which is not a Fredholm expansion. A somewhat similar looking formula was derived non-rigorously in a related model by Dotsenko.

40 pages. In the second version some errors have been corrected and some extra material has been added

References in corpus (3)

• Slow decorrelations in KPZ growth
• Reflected Brownian motions in the KPZ universality class
• A multi-dimensional Markov chain and the Meixner ensemble

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• Maximum of an Airy process plus Brownian motion and memory in KPZ growth
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