2024/03/15 by Benjamin Budway, Budway, Benjamin, Mykhaylo Shkolnikov +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #60H #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2403.10724
openalex publication_date 2024/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Multilevel Dyson Brownian motions (MDBMs) combine Dyson Brownian motions of different dimensions into a single process in a canonical way. This paper completes the theory of MDBMs for β≥2. Specifically, we use the superposition principle of Figalli and Trevisan to construct the MDBMs for all β>2 in a unified manner. This also extends their stochastic differential equation representation, first discovered by Gorin and Shkolnikov, to all β>2 and proves the uniqueness of the MDBMs for all β>2. Finally, we show that their limit as β\downarrow2 is given by the β=2 MDBM, commonly referred to as the Warren process.