On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
arXiv:1902.02216 · doi:10.1051/mmnp/2019033
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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- Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
- Planar elliptic growth
- Random Matrices in 2D, Laplacian Growth and Operator Theory
- Stochastic Loewner evolution driven by Levy processes
- Global properties of Stochastic Loewner evolution driven by Levy processes
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