The thesis focuses on processes on symplectic Gelfand-Tsetlin patterns. In chapter 4, a process with dynamics inspired by the Berele correspondence [Ber86] is presented. It is proved that the shape of the pattern is a Doob h-transform of independent random walks with h given by the symplectic Schur function. This is followed by an extension to a q-weighted version. This randomised version has itself a branching structure and is related to a q-deformation of the so2n+1-Whittaker functions. In chapter 5, we present a fully randomised process. This process q-deforms a process proposed in [WW09]. In chapter 7 we prove the convergence of the q-deformation of the so2n+1-Whittaker functions to the classical so2n+1-Whittaker functions when q → 1. Finally, in chapter 8 we turn our interest to the continuous setting and construct a process on patterns which contains a positive temperature analogue of the Dyson's Brownian motion of type B∕C. The processes obtained are h-transforms of Brownian motions killed at a continuous rate that depends on their distance from the boundary of the Weyl chamber of type B∕C, with h related with the so2n+1-Whittaker functions.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:725275 |
| Date | January 2016 |
| Creators | Nteka, Ioanna |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/93408/ |
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