Rate of Convergence in Multiple SLE using Random Matrix Theory

TL;DR

This paper establishes convergence rates for multiple SLE models driven by Dyson Brownian motion, integrating Schramm-Loewner Evolution techniques with random matrix theory to advance understanding of their hydrodynamic limits.

Contribution

It introduces a novel approach combining SLE and random matrix theory to analyze convergence rates in multiple SLE models with Dyson Brownian motion drivers.

Findings

Convergence order for multiple SLE with Dyson Brownian motion

Application of random matrix universality techniques to SLE

Unified framework for SLE convergence analysis

Abstract

We provide an order of convergence for a version of the Carath\'eodory convergence for the multiple SLE model with a Dyson Brownian motion driver towards its hydrodynamic limit, for $\beta=1$ and $\beta=2$. The result is obtained by combining techniques from the field of Schramm-Loewner Evolutions with modern techniques from random matrices. Our approach shows how one can apply modern tools used in the proof of universality in random matrix theory, in the field of Schramm-Loewner Evolutions.