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13 papers · 2 filters
Generalizations of Efron's theorem
Yannis Oudghiri
In this article, we prove two new versions of a theorem proven by Efron in [Efr65]. Efron's theorem says that if a function is non-decreasi…
Strong asymptotic freeness for independent uniform variables on compact groups associated to non-trivial representations
Charles Bordenave, Benoit Collins
Asymptotic freeness of independent Haar distributed unitary matrices was discovered by Voiculescu. Many refinements have been obtained, including strong asymptotic freeness of rand…
Convergence of the spectral radius of a random matrix through its characteristic polynomial
Charles Bordenave, Djalil Chafaï, David García-Zelada
Consider a square random matrix with independent and identically distributed entries of mean zero and unit variance. We show that as the dimension tends to infinity, the spectral r…
At the edge of a one-dimensional jellium
Djalil Chafaï, David García-Zelada, Paul Jung
We consider a one-dimensional classical Wigner jellium, not necessarily charge neutral, for which the electrons are allowed to exist beyond the support of the background charge. Th…
Markovian linearization of random walks on groups
Charles Bordenave, Bastien Dubail
In operator algebra, the linearization trick is a technique that reduces the study of a non-commutative polynomial evaluated at elements of an algebra A to the study of a polynomia…
Finding geodesics on graphs using reinforcement learning
Daniel Kious, Cécile Mailler, Bruno Schapira
It is well-known in biology that ants are able to find shortest paths between their nest and the food by successive random explorations, without any mean of communication other tha…