Stochastic Loewner Evolutions, Fuchsian Systems and Orthogonal Polynomials
Abstract
We find a wide class of Levy-Loewner evolutions for which the value of integral means beta-spectrum β(q) at q=2 is the maximal real eigenvalue of a three-diagonal matrix. The second moments of derivatives of corresponding conformal mappings are expressed through solutions of matrix Fuchsian systems with three singular points.
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