Local Functional Inequalities in One Dimensional Free Probability
  In this note we introduce and prove local and potential independent transportation, Log-Sobolev and HWI inequalities in one dimensional free probability on compact intervals which are sharp. We recover using this approach a free transportation inequality on the whole real line which was put forward recently by M. Maida and E. Maurel-Segala. 
Ionel Popescu
math.PR math.FA