125 citations · 759 across the 31 of their papers we have counts for
24 papers · 1 filter
Matrix Whittaker processes
Jonas Arista, Elia Bisi, Neil O'Connell
We study a discrete-time Markov process on triangular arrays of matrices of size , driven by inverse Wishart random matrices. The components of the right edge evolve as mu…
Matsumoto-Yor and Dufresne type theorems for a random walk on positive definite matrices
Jonas Arista, Elia Bisi, Neil O'Connell
We establish analogues of the geometric Pitman theorem of Matsumoto and Yor and of the classical Dufresne identity, for a multiplicative random walk on positive definite mat…
The Doob-McKean identity for stable Lévy processes
Andreas E. Kyprianou, Neil O'Connell
We re-examine the celebrated Doob--McKean identity that identifies a conditioned one-dimensional Brownian motion as the radial part of a 3-dimensional Brownian motion or, equivalen…
The geometric Burge correspondence and the partition function of polymer replicas
Elia Bisi, Neil O'Connell, Nikos Zygouras
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We establish its fundamental relation…
Scaling limits for non-intersecting polymers and Whittaker measures
Samuel G. G. Johnston, Neil O'Connell
We study the partition functions associated with non-intersecting polymers in a random environment. By considering paths in series and in parallel, the partition functions carry na…
Interacting diffusions on positive definite matrices
Neil O'Connell
We consider systems of Brownian particles in the space of positive definite matrices, which evolve independently apart from some simple interactions. We give examples of such proce…