Spectral Gap Inequalities in Product Spaces with Conservation Laws

Abstract

Following an idea introduced by Carlen, Carvalho and Loss [7] we propose a general strategy to prove Poincaré inequalities in product spaces with one or more conservation laws. The method is shown to yield alternative proofs of well known results, such as the diffusive bounds for the spectral gap of generalized exclusion and zero range processes. Other models are also discussed, including anisotropic exclusion processes, simple exclusion with site–disorder and Ginzburg–Landau processes, where this approach provides sharp spectral gap estimates apparently inaccessible by previously known techniques.