An Example of Intrinsic Randomness in Deterministic PDEs
- Authors: Franco Flandoli, Benjamin Gess, Francesco Grotto
- Preprint year: 2020
- First public date: 2020-12-08
- arXiv: 2012.04398
- Status: Published
- Publication type: Journal article
- Publication year: 2022
- Journal: Stochastics and dynamics, 22 (2022) 7, p. 2240023
- DOI: 10.1142/s0219493722400238
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.