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Logarithmic Sobolev inequality for zero-range dynamics: independence of the number of particles. (English) Zbl 1109.60080

Summary: 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 the square of \(L\), that is presented in a forthcoming paper.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
60E15 Inequalities; stochastic orderings
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