KP governs random growth off a one dimensional substrate
Probability
2023-04-26 v5 Mathematical Physics
math.MP
Abstract
The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev-Petviashvili (KP) equation. This is derived algebraically from a Fredholm determinant obtained in [MQR17, arXiv:1701.00018] for the KPZ fixed point as the limit of the transition probabilities of TASEP, a special solvable model in the KPZ universality class. The Tracy-Widom distributions appear as special self-similar solutions of KP and KdV. In addition, it is noted that several known exact solutions of the KPZ equation also solve KP.
Cite
@article{arxiv.1908.10353,
title = {KP governs random growth off a one dimensional substrate},
author = {Jeremy Quastel and Daniel Remenik},
journal= {arXiv preprint arXiv:1908.10353},
year = {2023}
}
Comments
Improved presentation, misprint corrected. 22 pages