Multilevel Dyson Brownian motions via the superposition principle

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 2. Specifically, we use the superposition principle of Figalli and Trevisan to construct the MDBMs for all >2 in a unified manner. This also extends their stochastic differential equation representation, first discovered by Gorin and Shkolnikov, to all >2 and proves the uniqueness of the MDBMs for all >2. Finally, we show that their limit as 2 is given by the =2 MDBM, commonly referred to as the Warren process.