Interlacing Diffusions

Abstract

We study in some generality intertwinings between $h$-transforms of Karlin-McGregor semigroups associated with one dimensional diffusion processes and those of their Siegmund duals. We obtain couplings so that the corresponding processes are interlaced and furthermore give formulae in terms of block determinants for the transition densities of these coupled processes. This allows us to build diffusion processes in the space of Gelfand-Tsetlin patterns so that the evolution of each level is Markovian. We show how known examples naturally fit into this framework and construct new processes related to minors of matrix valued diffusions. We also provide explicit formulae for the transition densities of the particle systems with one-sided collisions at either edge of such patterns.

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Cited by in corpus (6)

• One-sided reflected Brownian motions and the KPZ fixed point
• Last-passage time for linear diffusions and application to the emptying time of a box
• Determinantal structures in space inhomogeneous dynamics on interlacing arrays
• Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous and discrete time stochastic processes
• Exact solution of interacting particle systems related to random matrices
• Laguerre and Jacobi analogues of the Warren process