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Heat kernel upper bounds for interacting particle systems. (English) Zbl 1416.82029
Summary: We show a diffusive upper bound on the transition probability of a tagged particle in the symmetric simple exclusion process. The proof relies on optimal spectral gap estimates for the dynamics in finite volume, which are of independent interest. We also show off-diagonal estimates of Carne-Varopoulos type.

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
35B65 Smoothness and regularity of solutions to PDEs
60K35 Interacting random processes; statistical mechanics type models; percolation theory
35K05 Heat equation
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