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## Stochastic stability of traffic maps

We study ergodic properties of a family of traffic maps acting in

the space of bi-infinite sequences of real numbers. The corresponding

dynamics mimics the motion of vehicles in a simple traffic flow, which

explains the name. Using connections to topological Markov chains we obtain

nontrivial invariant measures, prove their stochastic stability, and

calculate the topological entropy. Technically these results in the

deterministic setting are related to the construction of measures of maximal

entropy via measures uniformly distributed on periodic points of a given

period, while in the random setting we directly construct (spatially) Markov

invariant measures. In distinction to conventional results the limiting

measures in non-lattice case are non-ergodic. Average velocity of individual

``vehicles'' as a function of their density and its stochastic stability is

studied as well.