Perturbations of Multiple Schramm-Loewner Evolution with Two Non-colliding Dyson Brownian Motions

2021/11/16 by Chen, Jiaming, Margarint, Vlad · 2 citations
#Complex Variables (math.CV) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.08522

Abstract

In this article, we study multiple SLE_κ, for κ∈(0,4], driven by Dyson Brownian motion. This model was introduced in the unit disk by Cardy in connection with the Calogero-Sutherland model. We prove the Carathéodory convergence of perturbed Loewner chains under different initial conditions and under different diffusivity κ∈ (0,4] for the case of N=2 driving forces. Our proofs use the analysis of Bessel processes and estimates on Loewner differential equation with multiple driving forces. In the last section, we estimate the Hausdorff distance of the hulls under perturbations of the driving forces, with assumptions on the modulus of the derivative of the multiple Loewner maps.

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• Fisher information and trajectorial interpretation to the Itô--Langevin relative entropy dissipation
• Splitting algorithm and normed convergence for drawing the random Loewner curves

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