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.
Bibliographical noteFunding Information:
* Research supported in part by NSF Grant No. DMS-0405587 and by EPSRC Visiting Fellowship. ** Research supported in part by NSF Grant No. DMS-9803239,DMS-0100289. t Research supported in part by NSF Grant No. DMS-0401239. Received January 27, 2004 and in revised form May 5, 2005