Logarithmic Sobolev Inequality for Zero-Range Dynamics: independence of   the number of particles
  We prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter L may depend on L but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as L^2, that will be presented in a forthcoming paper. 
Paolo Dai Pra and Gustavo Posta