Perturbations of multiple Schramm–Loewner evolution with two non-colliding Dyson Brownian motions
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Date
2022-09Type
- Journal Article
ETH Bibliography
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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. Show more
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publishedExternal links
Journal / series
Stochastic Processes and their ApplicationsVolume
Pages / Article No.
Publisher
ElsevierOrganisational unit
02000 - Dep. Mathematik / Dep. of Mathematics
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