Local-to-global functional inequalities in simplicial complexes

A study of random walks over simplicial complexes with a particular emphasis on matroids. A framework is developed that yields results on the entropy contraction and modified log-Sobolev constant of the exchange walks over the levels of a simplicial complex, on the basis of entropy contraction properties of some local walks. This provides a general method for analyzing a variety of Markov chains by analyzing some of their lower-dimensional instances.