Talagrand's concentration inequality
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In probability theory, Talagrand's concentration inequality is an isoperimetric-type inequality for product probability spaces. It was first proved by the French mathematician Michel Talagrand. The inequality is one of the manifestations of the concentration of measure phenomenon.
where is the complement of where this is defined by
and where is Talagrand's convex distance defined as
where , are -dimensional vectors with entries respectively and is the -norm. That is,
- Alon, Noga; Spencer, Joel H. (2000). The Probabilistic Method (2nd ed.). John Wiley & Sons, Inc. ISBN 0-471-37046-0.
- Ledoux, Michel (2001). The Concentration of Measure Phenomenon. American Mathematical Society. ISBN 0-8218-2864-9.
- Talagrand, Michel (1995). Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathématiques de l'IHÉS. Springer-Verlag. doi:10.1007/BF02699376. ISSN 0073-8301.
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