# An Example of Intrinsic Randomness in Deterministic PDEs

@inproceedings{Flandoli2020AnEO, title={An Example of Intrinsic Randomness in Deterministic PDEs}, author={Franco Flandoli and Benjamin Gess and Francesco Grotto}, year={2020} }

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 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.

## References

SHOWING 1-10 OF 34 REFERENCES

The KPZ fixed point

- MathematicsActa Mathematica
- 2021

An explicit Fredholm determinant formula is derived for the multipoint distribution of the height function of the totally asymmetric simple exclusion process with arbitrary initial condition. The…

Convergence of exclusion processes and the KPZ equation to the KPZ fixed point

- Mathematics
- 2020

We show that under the 1:2:3 scaling, critically probing large space and time, the height function of finite range asymmetric exclusion processes and the KPZ equation converge to the KPZ fixed point,…

From the butterfly effect to spontaneous stochasticity in singular shear flows

- Physics
- 2020

The butterfly effect is today commonly identified with the sensitive dependence of deterministic chaotic systems upon initial conditions. However, this is only one facet of the notion of…

Statistical determinism in non-Lipschitz dynamical systems

- Mathematics
- 2020

We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic…

The KPZ fixed point for discrete time TASEPs

- Mathematics
- 2020

We consider two versions of discrete time totally asymmetric simple exclusion processes (TASEPs) with geometric and Bernoulli random hopping probabilities. For the process mixed with these and…

From the totally asymmetric simple exclusion
process to the KPZ

- PhysicsRandom Matrices
- 2019

These are the lecture notes for the mini-course at the PCMI graduate summer school in 2017. These notes are based on the article by Matetski, Quastel and Remenik arXiv:1701.00018 and give a…

Solution of the Kolmogorov equation for TASEP

- Mathematics
- 2019

We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The…

KPZ Reloaded

- Mathematics
- 2017

We analyze the one-dimensional periodic Kardar–Parisi–Zhang equation in the language of paracontrolled distributions, giving an alternative viewpoint on the seminal results of Hairer. Apart from…

On global solutions of the random Hamilton-Jacobi equations and the KPZ problem

- Mathematics
- 2017

In this paper, we discuss possible qualitative approaches to the problem of KPZ universality. Throughout the paper, our point of view is based on the geometrical and dynamical properties of…

Mailybaev . Spontaneous stochasticity of velocity in turbulence models . Multiscale Modeling & Simulation

- A SIAM Interdisciplinary Journal
- 2016