Two time distribution in Brownian directed percolation
Mathematical Physics
2016-06-22 v2 math.MP
Probability
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.
Cite
@article{arxiv.1502.00941,
title = {Two time distribution in Brownian directed percolation},
author = {Kurt Johansson},
journal= {arXiv preprint arXiv:1502.00941},
year = {2016}
}
Comments
40 pages. In the second version some errors have been corrected and some extra material has been added