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Probability in Banach Spaces: Isoperimetry and Processes
Notation.- 0. Isoperimetric Background and Generalities.- 1. Isoperimetric Inequalities and the Concentration of Measure Phenomenon.- 2. Generalities on Banach Space Valued Random Variables and
Concentration of measure and isoperimetric inequalities in product spaces
The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product ΩN of probability spaces has measure at least one half, “most” of the points of Ωn are “close”
New concentration inequalities in product spaces
Abstract. We introduce three new ways to measure the “distance” from a point to a subset of a product space and we prove corresponding concentration inequalities. Each of them allows to control the
Transportation cost for Gaussian and other product measures
AbstractConsider the canonical Gaussian measure γN on ℝ, a probability measure μ on ℝN, absolutely continuous with respect to γN. We prove that the transportation cost of μ to γN, when the cost of
On Russo's Approximate Zero-One Law
Consider the product measure μ p on {0, 1} n , when 0 (resp. 1) is given weight 1-p (resp. p). Consider a monotone subset A of {0, 1} n . We give a precise quantitative form to the following
Spin Glasses: A Challenge for Mathematicians
Part of my standard advice to graduate students seeking a career in mathematics research is that, sometime during their second or third year, they should spend six months getting to grips with the