The stochastic Bessel operator at high temperatures

2024/11/21 by Hugo Magaldi, Magaldi, Hugo
Economics, Econometrics and Finance · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2411.13972

openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We know from Ramírez and Rider that the hard edge of the spectrum of the Beta-Laguerre ensemble converges, in the high-dimensional limit, to the bottom of the spectrum of the stochastic Bessel operator. Using stochastic analysis techniques, we show that, in the high temperatures limit, the rescaled eigenvalues point process of the stochastic Bessel operator converges to a limiting point process characterized with coupled stochastic dierential equations.

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