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We prove a weak law of large numbers for a tagged particle in a totally asymmetric exclusion process on the one-dimensional lattice. The particles are allowed to take long jumps but not pass each other. The object of the paper is to illustrate a special technique for proving such theorems. The method uses a coupling that mimics the HopfLax formula from the theory of viscosity solutions of Hamilton-Jacobi equations.

A variational coupling for a totally asymmetric exclusion process with long jumps but no passing