TY - JOUR AU - Miclo, Laurent PY - 2018/08/06 Y2 - 2024/03/29 TI - Some drawbacks of finite modified logarithmic Sobolev inequalities JF - MATHEMATICA SCANDINAVICA JA - Math. Scand. VL - 123 IS - 1 SE - Articles DO - 10.7146/math.scand.a-105279 UR - https://www.mscand.dk/article/view/105279 SP - 147-159 AB - <p>Classically, finite modified logarithmic Sobolev inequalities are used to deduce a differential inequality for the evolution of the relative entropy with respect to the invariant measure. We will check that these inequalities are ill-behaved with respect, on one hand, to the symmetrization procedure, and on the other hand, to the umbrella sampling procedure for Poincaré inequalities. A short spectral proof of the latter method is given to estimate the spectral gap of a finite reversible Markov generator $L$ in terms of the spectral gap of the restrictions of $L$ on two subsets whose union is the whole state space and whose intersection is not empty.</p> ER -