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arXiv · 1611.03247

Statistical mechanics of stochastic growth phenomena

Oleg Alekseev·Mark Mineev-Weinstein
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Abstract

We develop statistical mechanics for stochastic growth processes as applied to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasi-static) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with planar domains. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with the free-particle propagator on the infinite dimensional complex manifold with the Kähler metric.

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BibTeXRIS

Oleg Alekseev, Mark Mineev-Weinstein. 2017-10-06. Statistical mechanics of stochastic growth phenomena. https://doi.org/10.1103/physreve.96.010103

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