The directed landscape

The directed landscape

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Duncan Dauvergne, Princeton University
Fine Hall 214

I will describe the construction of the full scaling limit of (Brownian) last passage percolation: the directed landscape. The directed landscape can be thought of as a random scale-invariant `directed' metric on the plane, and last passage paths converge to directed geodesics in this metric. The directed landscape is expected to be a universal scaling limit for general last passage and random growth models (e.g. TASEP, the KPZ equation, the longest increasing subsequence in a random permutation). Joint work with Janosch Ortmann and Balint Virag.