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 $\mathbb{R}$. 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:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.04398
- arXiv:
- arXiv:2012.04398
- Bibcode:
- 2020arXiv201204398F
- Keywords:
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- Mathematics - Probability;
- Mathematical Physics
- E-Print:
- 25 pages