TY - JOUR

T1 - Statistical mechanics of stochastic growth phenomena

AU - Alekseev, Oleg

AU - Mineev-Weinstein, Mark

PY - 2017/7/20

Y1 - 2017/7/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85025631526&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.010103

DO - 10.1103/PhysRevE.96.010103

M3 - Article

AN - SCOPUS:85025631526

VL - 96

JO - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 010103

ER -