2023/12/05 by Elias Hess-Childs, Hess-Childs, Elias · 1 citation
Mathematics · Physics and Astronomy · #60F10 #60H30 #60K35 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2312.02904
openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We combine hydrodynamic and modulated energy techniques to study the large deviations of systems of particles with pairwise singular repulsive interactions and additive noise. Specifically, we examine periodic Riesz interactions indexed by parameter s∈[0,d-2) for d≥ 3 on the torus. When s∈(0,d-2), we establish a large deviation principle (LDP) upper bound and partial lower bound given sufficiently strong convergence of the initial conditions. When s=0 (i.e., the interaction potential is logarithmic), we prove that a complete LDP holds. Additionally, we show a local LDP holds in the distance defined by the modulated energy.