Leírás
Előadó: Virág Bálint
Cím: The Directed Landscape
Absztrakt: 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.