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Positive temperature dynamics on Gelfand-Tsetlin patterns restricted by wall
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Nteka, Ioanna (2016) Positive temperature dynamics on Gelfand-Tsetlin patterns restricted by wall. PhD thesis, University of Warwick.
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WRAP_Theses_Nteka_2016.pdf - Submitted Version - Requires a PDF viewer. Download (1179Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3104002~S15
Abstract
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.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Stochastic processes, Probabilities -- Mathematical models, Polynomials, Random walks (Mathematics) | ||||
| Official Date: | September 2016 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Department of Statistics | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Warren, Jonathan ; Zygouras, Nikos | ||||
| Format of File: | |||||
| Extent: | v, 139 leaves : illustrations | ||||
| Language: | eng |
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