9 citations · 51 across the 13 of their papers we have counts for
6 papers · 1 filter
Quantized Laplacian growth, III: On conformal field theories of Laplacian growth
Oleg Alekseev
A one-parametric stochastic dynamics of the interface in the quantized Laplacian growth with zero surface tension is introduced. The quantization procedure regularizes the growth b…
Quantized Laplacian growth, I: Statistical theory of Laplacian growth
Oleg Alekseev
We regularize the Laplacian growth problem with zero surface tension by introducing a short-distance cutoff , so that the change of the area of domains is quantized and equa…
Quantized Laplacian growth, II: 1D hydrodynamics of the Loewner density
Oleg Alekseev
A systematic analytic treatment of fluctuations in Laplacian growth is given. The growth process is regularized by a short-distance cutoff preventing the cusps production i…
Statistical mechanics of stochastic growth phenomena
Oleg Alekseev, Mark Mineev-Weinstein
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…
Theory of stochastic Laplacian growth
Oleg Alekseev, Mark Mineev-Weinstein
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 co…
Stochastic Laplacian growth
Oleg Alekseev, Mark Mineev-Weinstein
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all p…