Two time distribution in Brownian directed percolation

Understand

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.