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↓2 is given by the β=2 MDBM, commonly referred to as the Warren process.
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Budway et al. (2024) studied this question.
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