Theory of Stochastic Laplacian Growth

Oleg Alekseev, Mark Mineev-Weinstein

    Результат исследований: Научные публикации в периодических изданияхстатья

    3 Цитирования (Scopus)

    Выдержка

    We generalize the diffusion-limited aggregation by issuing many randomly-walking particles, which stick to a cluster at the discrete time unit providing its growth. Using simple combinatorial arguments we determine probabilities of different growth scenarios and prove that the most probable evolution is governed by the deterministic Laplacian growth equation. A potential-theoretical analysis of the growth probabilities reveals connections with the tau-function of the integrable dispersionless limit of the two-dimensional Toda hierarchy, normal matrix ensembles, and the two-dimensional Dyson gas confined in a non-uniform magnetic field. We introduce the time-dependent Hamiltonian, which generates transitions between different classes of equivalence of closed curves, and prove the Hamiltonian structure of the interface dynamics. Finally, we propose a relation between probabilities of growth scenarios and the semi-classical limit of certain correlation functions of “light” exponential operators in the Liouville conformal field theory on a pseudosphere.

    Язык оригиналаанглийский
    Страницы (с-по)68-91
    Число страниц24
    ЖурналJournal of Statistical Physics
    Том168
    Номер выпуска1
    DOI
    СостояниеОпубликовано - 1 июл 2017

    Отпечаток

    Pseudosphere
    Interface Dynamics
    Combinatorial argument
    nonuniform magnetic fields
    Diffusion-limited Aggregation
    Scenarios
    Normal matrix
    Tau Functions
    walking
    Semiclassical Limit
    Hamiltonian Structure
    Closed curve
    Conformal Field Theory
    Probable
    hierarchies
    equivalence
    Correlation Function
    Theoretical Analysis
    Discrete-time
    Ensemble

    Предметные области Scopus

    • Статистическая и нелинейная физика
    • Математическая физика

    Цитировать

    Alekseev, Oleg ; Mineev-Weinstein, Mark. / Theory of Stochastic Laplacian Growth. В: Journal of Statistical Physics. 2017 ; Том 168, № 1. стр. 68-91.
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    Theory of Stochastic Laplacian Growth. / Alekseev, Oleg; Mineev-Weinstein, Mark.

    В: Journal of Statistical Physics, Том 168, № 1, 01.07.2017, стр. 68-91.

    Результат исследований: Научные публикации в периодических изданияхстатья

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