Large deviations of Dyson Brownian motion on the circle and multiradial SLE(0+)

2024/07/18 by Abuzaid, Osama, Healey, Vivian Olsiewski, Peltola, Eveliina · 3 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.13762

Abstract

We show a finite-time large deviation principle (LDP) for "Dyson type" diffusion processes, including Dyson Brownian motion on the circle, for a fixed number of particles as the coupling parameter β=8/κ tends to ∞. We also characterize the large-time behavior of finite-energy and zero-energy systems. Interestingly, the latter correspond to the Calogero-Moser-Sutherland integrable system. We use these results to derive an LDP in the Hausdorff metric for multiradial Schramm-Loewner evolution, SLE_κ, as κ→ 0, with good rate function being the multiradial Loewner energy. Here, the main difficulty is that the curves have a common target point, preventing the configurational (global) approach. Our proof thus requires topological results in Loewner theory: using a derivative estimate for the radial Loewner map in terms of the energy of its driving function, we show that finite-energy multiradial Loewner hulls are disjoint unions of simple curves, except possibly at their common endpoint.

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• Coupling of radial multiple SLE with Gaussian free field, and the hydrodynamic limit
• Onsager--Machlup functional for multiple SLEs

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