Queues, stationarity, and stabilisation of last passage percolation (Joint work with Ofer Busani and Timo Seppäläinen)

(the seminar was postponed from an earlier date)

Take a point x on the 2-dimensional integer lattice and another one y North-East from the first. Now place independent identically distributed exponential weights on the vertices of the lattice; the last passage time between the two points is the maximal sum of these weights which can be collected by a path that takes North and East steps. The process of these weights as y varies is a difficult one, but, locally, has a nice asymptotic structure.

I'll explain what stationary queues have to do with this, and how this insight gives coalescence properties of the maximal-weight paths of last passage.