05598043

j

05598043 Miclo, Laurent An asymptotic condition for computing the logarithmic Sobolev constant on the line. (Une condition asymptotique pour le calcul de constantes de Sobolev logarithmiques sur la droite.) Ann. Inst. Henri Poincar\'e, Probab. Stat. 45, No. 1, 146-156 (2009). 2009 Association des Publications de l'Institut Henri Poincar\'e, Paris; Institut of Mathematical Statistics (IMS), Bethesda MD FR logarithmic Sobolev inequality Poincar\'e's inequality Hardy inequality integer-valued birth and death process

doi:10.1214/07-AIHP158

Summary: An explicit formula for the logarithmic Sobolev constant relative to real diffusions or to integer-valued birth and death processes is presented, under an asymptotic assumption for quantities naturally associated to Hardy inequalities in this context. Taking into account exact comparisons between entropy and appropriate variances, the proof goes back to Poincar\'e's inequality situation.