The subgaussian constant and concentration inequalities
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We study concentration inequalities for Lipschitz functions on graphs by estimating the optimal constant in exponential moments of subgaussian type. This is illustrated on various graphs and related to various graph constants. We also settle, in the affirmative, a question of Talagrand on a deviation inequality for the discrete cube.
KeywordsLipschitz Function Isoperimetric Inequality Logarithmic Sobolev Inequality Isoperimetric Problem Expander Graph
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- [B] S. G. Bobkov,On deviations from medians, Manuscript (1998)Google Scholar
- [B-H2] S. G. Bobkov and C. Houdré,Characterization of Gaussian measures in terms of the isoperimetric properties of half-spaces, Zap. Nauchn. Semin. S.-Petersburg. Otdel. Mat. Inst. im. V.A. Steklova RAN228 (1996) 31–38 (in Russian). English translation: Journal of Mathematical Sciences (New York)93 (1999), 270–275.Google Scholar
- [BHT] S. G. Bobkov, C. Houdré and P. Tetali,The subguassian constant and concentration inaqualities, Expanded version available at http://www.math.gatech.edu/~tetali/PUBLIS/BHT_SUB_full.texGoogle Scholar
- [J-S] K. Jogdeo and S. M. Samuels,Monotone convergence of binomial probabilities and a generalization of Ramanujan's equation, American Mathematical Society39 (1968), 1191–1195.Google Scholar
- [McD] C. McDiarmid,On the method of bounded differences, inSurveys in Combinatorics, London Mathematicsl Society Lecture Notes, Vol. 141, Cambridge University Press, 1989, pp. 148–188.Google Scholar
- [P] G. Pisier,Probabilistic methods in the geometry of Banach spaces, inProbability and Analysis, Varenna (Italy) 1985, Lecture Notes in Mathematics1206, Springer, Berlin, 1986, pp. 167–241.Google Scholar
- [S] L. Saloff-Coste,Lectures on finite Markov chains, Ecole d'Eté de Probabilités de St-Flour (1996), Lecture Notes in Mathematics1665, Springer, Berlin, 1997, pp. 301–413.Google Scholar
- [S-T] M. Sammer and P. Tetali,Concentration on the discrete torus using transportation, submitted (2005).Google Scholar
- [St] S. Stoyanov,Isoperimetric and Related Constants for Graphs and Markov chains, Ph.D. thesis, Georgia Institute of Technology, 2001.Google Scholar