Statistical mechanics of stochastic growth phenomena

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.

6 pages, 1 figure; v2: exposition improved

References in corpus (4)

• Normal random matrix ensemble as a growth problem
• Large N expansion for the 2D Dyson gas
• Theory of stochastic Laplacian growth
• Stochastic Laplacian growth

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• Field theoretical approach for signal detection in nearly continuous positive spectra I: Matricial data
• Quantized Laplacian growth, II: 1D hydrodynamics of the Loewner density
• Integrability-preserving regularizations of Laplacian Growth