On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth

Published 6 Feb 2019 in math-ph, cond-mat.stat-mech, math.MP, math.PR, nlin.PS, and nlin.SI | (1902.02216v2)

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.

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