An example of intrinsic randomness in deterministic PDES

Abstract

A new mechanism leading to a random version of Burgers’ equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically stochastic, non-entropic weak solution of Burgers’ equation on [Formula: see text]. In this interpretation, the appearance of randomness in the Burgers’ dynamics is caused by random additions of jumps to the solution, corresponding to the random effects in TASEP.