English

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}
}