Large deviation bounds for matrix Brownian motion

By Philippe Biane, Mireille Capitaine, Alice Guionnet. 2003

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Free Probability and Random Matrices (2014, background): “Though we do not know at the moment whether χ = χ∗ in general, we have at least one half of this by the following deep result of Biane, Capitaine, and Guionnet [38].”
A free stochastic partial differential equation (2010, background): “,Xn), known by the fundamental work [2] to be greater than the previous microstate entropy, and believed to be equal (at least modulo Connes’ embedding conjecture).”
L 2-homology for von Neumann algebras (2003, methodology): “This unexpected connection allows us to rely on several deep results in free probability theory, including the inequality between the microstates and microstates-free free entropy proved by recent fundamental work of Biane, Capitaine and Guionnet [BCG03].”