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Freeness of type and conditional freeness for random matrices
Guillaume Cébron, Antoine Dahlqvist, Franck Gabriel
The asymptotic freeness of independent unitarily invariant random matrices holds in expectation up to . An already known consequence is the infinitesimal fre…
Geometric stochastic heat equations
Yvain Bruned, Franck Gabriel, Martin Hairer +1
We consider a natural class of -valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorph…
Large permutation invariant random matrices are asymptotically free over the diagonal
Benson Au, Guillaume Cébron, Antoine Dahlqvist +2
We prove that independent families of permutation invariant random matrices are asymptotically free over the diagonal, both in probability and in expectation, under a uniform bound…
A combinatorial theory of random matrices III: random walks on , ramified coverings and the Yang-Mills measure
Franck Gabriel
The aim of this article is to study some asymptotics of a natural model of random ramified coverings on the disk of degree . We prove that the monodromy field, called also the h…
Combinatorial theory of permutation-invariant random matrices II: cumulants, freeness and Levy processes
Franck Gabriel
The -tracial algebras are algebras endowed with multi-linear forms, compatible with the product, and indexed by partitions. Using the notion of -cumulants…