Description
I will talk about Brownian last passage percolation and its full
scaling limit we recently constructed with Dauvergne and Ortmann.
– Last passage paths converge to random continuous functions which are
more regular than Brownian motion: 2/3-eps Holder. They are geodesics
in the directed landscape.
The scaling limit of the longest increasing subsequence of a random
permutation is also given by these geodesics.
– The directed landscape is a stationary independent-increment process
on the metric composition semigroup. It has the famous 1-2-3 scaling.
– The directed landscape contains all the desired information in the
limit. Previous constructions, such as the Airy line ensemble, the KPZ
fixed point and multi-time limits are all marginals of this process.