Subgaussian 1-cocycles on discrete groups

Abstract

We prove the $L_p$ Poincaré inequalities with constant $C\sqrt{p}$ for $1$-cocycles on countable discrete groups under Bakry--Emery's ${\Gamma }_2$-criterion. These inequalities determine an analogue of subgaussian behavior for 1-cocycles. Our theorem improves some of our previous results in this direction, and in particular implies Efraim and Lust-Piquard's Poincaré type inequalities for the Walsh system. The key new ingredient in our proof is a decoupling argument. As complementary results, we also show that the spectral gap inequality implies the $L_p$ Poincaré inequalities with constant $Cp$ under some conditions in the noncommutative setting. New examples which satisfy the ${\Gamma }_2$-criterion are provided as well.

29 pages

References in corpus (1)

• Poincaré type inequalities on the discrete cube and in the CAR algebra

Cited by in corpus (3)

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