Transport inequalities and Concentration of measure

Concentration of measure and logarithmic Sobolev inequalities

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Measure Concentration, Transportation Cost, and Functional Inequalities

— In these lectures, we present a triple description of the concentration of measure phenomenon, geometric (through BrunnMinkoswki inequalities), measure-theoretic (through transportation cost inequalities) and functional (through logarithmic Sobolev inequalities), and investigate the relationships between these various viewpoints. Special emphasis is put on optimal mass transportation and the ...

Concentration of Measure Inequalities in Information Theory, Communications, and Coding Concentration of Measure Inequalities in Information Theory, Communications, and Coding

During the last two decades, concentration inequalities have been the subject of exciting developments in various areas, including convex geometry, functional analysis, statistical physics, high-dimensional statistics, pure and applied probability theory (e.g., concentration of measure phenomena in random graphs, random matrices, and percolation), information theory, theoretical computer scienc...

Concentration - of - measure inequalities Lecture notes

Concentration of Measure Inequalities in Information Theory, Communications and Coding

Concentration inequalities have been the subject of exciting developments during the last two decades, and they have been intensively studied and used as a powerful tool in various areas. These include convex geometry, functional analysis, statistical physics, statistics, pure and applied probability theory (e.g., concentration of measure phenomena in random graphs, random matrices and percolat...