9 citations · 51 across the 13 of their papers we have counts for
14 papers
Quenched Growth of Normal Matrices and Harmonic Measure
Oleg Alekseev
The eigenvalues of a large normal random matrix form a two-dimensional Coulomb gas. At fixed weight, the spectral droplet grows with the matrix rank, and its semiclassical density…
Multi-point passage probabilities and Green's functions for SLE
Oleg Alekseev
We consider a loop representation of the model at the critical point. When the model represents ensembles of self-avoiding loops (i.e., it corresponds to SLE with $κ=8…
Martingales of stochastic Laplacian growth
Oleg Alekseev
A family of exponential martingales of a stochastic Laplacian growth problem is proposed. Stochastic Laplacian growth describes a regularized interface dynamics in a two-fluid syst…
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…
Wilson Loop Invariants from Conformal Blocks
Oleg Alekseev, Fábio Novaes
Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invaria…
Form factors of descendant operators in the Bullough-Dodd model
Oleg Alekseev
We propose a free field representation for the form factors of descendant operators in the Bullough-Dodd model. This construction is a particular modification of Lukyanov's techniq…
Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field
Oleg Alekseev
We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the co…
Form factors of descendant operators: affine Toda theory
Oleg Alekseev, Michael Lashkevich
In the framework of the free field representation we obtain exact form factors of local operators in the two-dimensional affine Toda theories of the series. The con…
Ring of physical states in the M(2,3) Minimal Liouville gravity
O. Alekseev, M. Bershtein
We consider the M(2,3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construc…