Hypercontractivity and Gaussian isoperimetry. Applications to spin systems (Q1592253)

The author establishes a Gaussian isoperimetric inequality for a hypercontractive reversible diffusion generator on a compact Riemann manifold. The method of proof also allows to derive an isoperimetric inequality, weaker than that of S. Bobkov, for a hypercontractive reversible generator on a finite set. Applications are given to discrete spin systems of infinite range where exponential decay of correlations holds. For related work see \textit{E. Laroche} [Probab. Theory Relat. Fields 101, No. 1, 89-132 (1995; Zbl 0820.60082)].