649 citations · 2.6k across the 83 of their papers we have counts for
5 papers · 1 filter
On spectral distribution of sample covariance matrices from large dimensional and large -fold tensor products
Benoît Collins, Jianfeng Yao, Wangjun Yuan
We study the eigenvalue distributions for sums of independent rank-one -fold tensor products of large -dimensional vectors. Previous results in the literature assume that $k=…
Projections of Orbital Measures and Quantum Marginal Problems
Benoît Collins, Colin McSwiggen
This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix…
The Weingarten Calculus
Benoit Collins, Sho Matsumoto, Jonathan Novak
This is a short introduction to Weingarten Calculus. Weingarten Calculus is a method to compute the joint moments of matrix variables distributed according to the Haar measure of c…
Asymptotic Freeness of Layerwise Jacobians Caused by Invariance of Multilayer Perceptron: The Haar Orthogonal Case
Benoit Collins, Tomohiro Hayase
Free Probability Theory (FPT) provides rich knowledge for handling mathematical difficulties caused by random matrices that appear in research related to deep neural networks (DNNs…
Convergence for noncommutative rational functions evaluated in random matrices
Benoît Collins, Tobias Mai, Akihiro Miyagawa +2
One of the main applications of free probability is to show that for appropriately chosen independent copies of random matrix models, any noncommutative polynomial in these …