Perturbations of multiple Schramm–Loewner evolution with two non-colliding Dyson Brownian motions

Jiaming Chen and Vlad Margarint

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 553-570

Abstract: In this article we study multiple SLEκ, for κ∈(0,4], driven by Dyson Brownian motions. This model was introduced in the unit disk by Cardy, (2003) 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.

Keywords: Multiple SLE; Dyson Brownian motion; Bessel processes (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:151:y:2022:i:c:p:553-570

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DOI: 10.1016/j.spa.2022.06.014

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