On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
Mathematical Physics
2020-02-17 v2 Statistical Mechanics
math.MP
Probability
Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
Abstract
We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions.
Keywords
Cite
@article{arxiv.1902.02216,
title = {On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth},
author = {Igor Loutsenko and Oksana Yermolayeva},
journal= {arXiv preprint arXiv:1902.02216},
year = {2020}
}