On a result of David Aldous concerning the trees in a conditioned excursion.
Dyson's Brownian motions, intertwining and interlacing.
The noise made by a Poisson snake.
Some examples of dynamics for Gelfand-tsetlin patterns.
Maximum of Dyson Brownian motion and non-colliding systems with a boundary.
Interlaced processes on the circle
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned...
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