t^{1/3} fluctuation around the shock of TASEP with random initial condition
Probability
2024-09-26 v1
Abstract
The totally asymmetric exclusion process (TASEP) is one of the solvable models in the KPZ universality class. When TASEP starts with the product Bernoulli measure with a smaller density on the left of the origin, it presents shocks in the evolution. For a long time, it has been known that fluctuations are the product of Gaussians on the scale t^{1/2} due to initial randomness. In this paper, we will describe how to see the t^{1/3} fluctuations for these initial conditions.
Cite
@article{arxiv.2409.16989,
title = {t^{1/3} fluctuation around the shock of TASEP with random initial condition},
author = {Xincheng Zhang},
journal= {arXiv preprint arXiv:2409.16989},
year = {2024}
}
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42 pages