Ma, Yu Tao et al., Logarithmic Sobolev, isoperimetry and transport inequalities on graphs, Acta mathematica Sinica. English series (Print) , 32(10), 2016, pp. 1221-1236
In this paper, we study some functional inequalities (such as Poincaré inequality, logarithmic Sobolev inequality, generalized Cheeger isoperimetric inequality, transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of (random) path method. We provide estimates of the involved constants.