6 papers
Functional inequalities for Boolean entropy
Guillaume Cébron, Kewei Pan
Building on the recently introduced notion of Boolean entropy, we define the corresponding Boolean Fisher information via a de Bruijn identity. We study the monotonicity of this Fi…
Combinatorics of cyclic-conditional freeness
Octavio Arizmendi, Guillaume Cébron, Nicolas Gilliers
This work investigates the combinatorial structures underlying cyclic conditional freeness and introduces cumulants that serve to linearize the cyclic conditional additive convolut…
Infinitesimal freeness for orthogonally invariant random matrices
Guillaume Cébron, James A Mingo
We introduce a new kind of free independence, called real infinitesimal freeness. We show that independent orthogonally invariant with infinitesimal laws are asymptotically real in…
Strong Convergence of Multiplicative Brownian Motions on the General Linear Group
Marwa Banna, Mireille Capitaine, Guillaume Cébron
We consider the family of multiplicative Brownian motions on the general linear group introduced by Driver-Hall-Kemp. They are parametrized by the real variance $λ\in…
Central limit theorem for -independent products and higher-order tensors
Guillaume Cébron, Patrick Oliveira Santos, Pierre Youssef
We establish a central limit theorem (CLT) for families of products of -independent random variables. We utilize graphon limits to encode the evolution of independence and char…
Graphon-Theoretic Approach to Central Limit Theorems for -Independence
Guillaume Cébron, Patrick Oliveira Santos, Pierre Youssef
We establish a central limit theorem for the sum of -independent random variables, extending both the classical and free probability setting. Central to our approach is the use…