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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…
Combinatorial theory of permutation-invariant random matrices I: partitions, geometry and renormalization
Franck Gabriel
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structu…
Planar Markovian Holonomy Fields
Franck Gabriel
We study planar random holonomy fields which are processes indexed by paths on the plane which behave well under the concatenation and orientation-reversing operations on paths. We…