arXiv subjects

Vladislav Guskov

Publications and source records attributed to Vladislav Guskov.

4 recordsLinked to original sources

arXiv2026

Dyson Brownian motion on a Jordan curve

Zabrodin recently proposed a generalization of Dyson Brownian motion to a setting where the particles are confined to a smooth Jordan curve in the plane. In this paper, we discuss a rigorous construction of such a process on a rectifiable Jordan curve and study some of its basic properties. Under further smoothness assumptions, we derive the associated Fokker-Planck-Kolmogorov equation, prove convergence towards the stationary Coulomb gas distribution, study large deviations at low temperature, and derive the limiting mean-field McKean--Vlasov equation in the many-particle limit.

math.PR↗

arXiv2025

Loewner--Kufarev entropy and large deviations of the Hastings--Levitov model

We consider the Hastings--Levitov HL(0) model in the small particle scaling limit and prove a large deviation principle. The rate function is given by the relative entropy of the driving measure $ρ$ for the Loewner--Kufarev equation: \[ H(ρ) = \frac{1}{2π}\iint \barρ_t(θ) \log \barρ_t(θ) dθdt, \] whenever $ρ= \barρ_t dθdt/2π$ with $\int_{S^1} \barρ_t dθ/2π= 1$. We investigate the class of shapes that can be generated by finite entropy Loewner evolution and show that it contains all Weil-Petersson quasicircles, all Becker quasicircles, a Jordan curve with a cusp, and a non-simple curve. We also consider the problem of finding a measure of minimal entropy generating a given shape as well as a simplified version of the problem for a related transport equation.

math.PR↗

arXiv2022

A large deviation principle for the Schramm-Loewner evolution in the uniform topology

We establish a large deviation principle for chordal SLE$_κ$ parametrized by capacity, as the parameter $κ\to 0+$, in the topology generated by uniform convergence on compact intervals of the positive real line. The rate function is shown to equal the Loewner energy of the curve. This strengthens the recent result of E. Peltola and Y. Wang who obtained the analogous statement using the Hausdorff topology.

math.PR↗

arXiv2020

Microscopic electron dynamics in nonlinear optical response of solids

We investigate the microscopic properties of the nonlinear optical response of crystalline solids within Floquet theory, and demonstrate that optically-induced microscopic charge distributions display complex spatial structure and nontrivial properties. Their spatial symmetry and temporal behavior are governed by crystal symmetries. We find that even when a macroscopic optical response of a crystal is forbidden, the microscopic optical response can, in fact, be nonzero. In such a case, the optically-induced charge redistribution can be considerable, even though the corresponding Fourier component of the time-dependent dipole moment per unit cell vanishes. We develop a method that makes it possible to completely reconstruct the microscopic optically-induced charge distributions by means of subcycle-resolved x-ray-optical wave mixing. We also show how, within this framework, the direction of the instantaneous microscopic optically-induced electron current flow can be revealed.

quant-ph↗