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, nonentropic weak solution of Burgers' equation on $\mathbb{R}$. 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.04398
 arXiv:
 arXiv:2012.04398
 Bibcode:
 2020arXiv201204398F
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 25 pages