Olivier Guédon Concentration phenomena in high dimensional geometry
نویسندگان
چکیده
Teo Banica Block-modified Wishart matrices and free Poisson laws We study the random matrices of type W̃ = (id ⊗ φ)W , where W is a complex Wishart matrix of parameters (dn, dm), and φ : Mn(C) → Mn(C) is a self-adjoint linear map. We prove that, under suitable assumptions, we have the d→∞ eigenvalue distribution formula δmW̃ ∼ πmnρ ν, where ρ is the law of φ, viewed as a square matrix, π is the free Poisson law, ν is the law of D = φ(1), and δ = tr(D). (Joint work with Ion Nechita.)
منابع مشابه
Concentration phenomena in high dimensional geometry
The purpose of this note is to present several aspects of concentration phenomena in high dimensional geometry. At the heart of the study is a geometric analysis point of view coming from the theory of high dimensional convex bodies. The topic has a broad audience going from algorithmic convex geometry to random matrices. We have tried to emphasize different problems relating these areas of res...
متن کاملProbability and Geometry in High Dimensions
The aim of this workshop is to reflect on recent developments in Probability and Geometry in High Dimensions with emphasis on interactions with other fields of mathematics such as compressed sensing, sparse statistical problems, random matrices, and empirical processes. We wish you a pleasant stay at Université Paris-Est Marne-la-Vallée.
متن کاملLp moments of random vectors via majorizing measures
For a random vector X in Rn, we obtain bounds on the size of a sample, for which the empirical p-th moments of linear functionals are close to the exact ones uniformly on a convex body K ⊂ Rn. We prove an estimate for a general random vector and apply it to several problems arising in geometric functional analysis. In particular, we find a short Lewis type decomposition for any finite dimension...
متن کاملA Probabilistic Approach to the Geometry of the `p Ball
This article investigates, by probabilistic methods, various geometric questions on B p , the unit ball of ` n p . We propose realizations in terms of independent random variables of several distributions on B p , including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B p . As another applicati...
متن کاملA Probabilistic Approach to the Geometry of the lp Ball
This article investigates, by probabilistic methods, various geometric questions on B p , the unit ball of l p . We propose realizations in terms of independent random variables of several distributions on B p , including the normalized volume measure. These representations allow us to unify and extend the known results of the sub-independence of coordinate slabs in B p . As another application...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012