We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand’s transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient conditions work even in the case where the Bakry-Emery curvature is not lower bounded. Several new examples are provided.

D E Furst, F C Breedveld, J R Kalden, J S Smolen, G R Burmester, M Dougados, P Emery, A Gibofsky, A F Kavenaugh, E C Keystone, L Klareskog, A S Russell, L B A van de Putte, M H Weisman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Wilson Truccolo, Uri T. Eden, 2,3 Matthew R. Fellows, John P. Donoghue, and Emery N. Brown Neuroscience Department, Brown University, Providence, Rhode Island; Neuroscience Statistics Research Laboratory, Department of Anesthesia and Critical Care, Massachusetts General Hospital, Boston; and Division of Health Sciences and Technology, Harvard Medical School/Massachusetts Institute of Technology...