13 citations · 36 across the 10 of their papers we have counts for
7 papers · 1 filter
Equilibrium of Charges and Differential Equations Solved by Polynomials II
Igor Loutsenko, Oksana Yermolayeva
We continue study of equilibrium of two species of 2d coulomb charges (or point vortices in 2d ideal fluid) started in (Igor Loutsenko, J. Phys. A: Math. Gen. 37, 1309, 2004). Alth…
Vortices and Factorization
Igor Loutsenko, Oksana Yermolayeva
We review applications of factorization methods to the problem of finding stationary point vortex patterns in two-dimensional fluid mechanics. Then we present a new class of patter…
Stochastic Loewner Evolutions, Fuchsian Systems and Orthogonal Polynomials
Igor Loutsenko, Oksana Yermolayeva
We find a wide class of Levy-Loewner evolutions for which the value of integral means beta-spectrum at is the maximal real eigenvalue of a three-diagonal matrix. The s…
On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth
Igor Loutsenko, Oksana Yermolayeva
We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical me…
On Harmonic Measure of the Whole Plane Levy-Loewner Evolution
Igor Loutsenko, Oksana Yermolayeva
Levy-Loewner evolution (LLE) is a generalization of the Schramm-Loewner evolution (SLE) where the branching is possible in a course of growth process. We consider a class of radial…
On Exact Multi-fractal Spectrum of the Whole-Plane SLE
Igor Loutsenko, Oksana Yermolayeva
We consider the whole-plane Shramm-Loewner evolution. Using exact solutions of fundamental equations for moments of derivative of conformal mappings we determine its average integr…