Statistical mechanics of stochastic growth phenomena

Oleg Alekseev, Mark Mineev-Weinstein

    Research output

    2 Citations (Scopus)


    We develop statistical mechanics for stochastic growth processes and apply it 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 (quasistatic) 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 simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a Kähler metric.

    Original languageEnglish
    Article number010103
    JournalPhysical Review E
    Issue number1
    Publication statusPublished - 20 Jul 2017

    Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Condensed Matter Physics

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