Bounds on the deficit in the logarithmic Sobolev inequality
  The de cit in the logarithmic Sobolev inequality for the Gaussian measure is considered and estimated by means of transport and information-theoretic distances. 
Sergey Bobkov (UMN-MATH), Nathael Gozlan (LAMA), Cyril Roberto   (MODAL'X), Paul-Marie Samson (LAMA)
math.PR math.FA