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math.PR2018
Topologies of random geometric complexes on Riemannian manifolds in the thermodynamic limit
Antonio Auffinger, Antonio Lerario, Erik Lundberg
We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence…
math.PR2018
The lemniscate tree of a random polynomial
Michael Epstein, Boris Hanin, Erik Lundberg
To each generic complex polynomial there is associated a labeled binary tree (here referred to as a "lemniscate tree") that encodes the topological type of the graph of $|p(…