# On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth

## TL;DR

This paper reviews how integrable systems theory applies to free-boundary fluid mechanics problems and stochastic models like Schramm-Loewner evolution, highlighting exact results in Laplacian growth.

## Contribution

It provides a comprehensive overview of classical and quantum integrable systems in fluid and statistical mechanics, emphasizing new exact solutions and their applications.

## Key findings

- Exact solutions in multi-fractal spectra of stochastic models
- Connections between integrable systems and Laplacian growth
- Review of applications to fluid mechanics and statistical models

## 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.