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Random polymers via orthogonal Whittaker and symplectic Schur functions
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Bisi, Elia (2018) Random polymers via orthogonal Whittaker and symplectic Schur functions. PhD thesis, University of Warwick.
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WRAP_Theses_Bisi_2018.pdf - Submitted Version - Requires a PDF viewer. Download (2654Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3367448~S15
Abstract
This thesis deals with some (1 + 1)-dimensional la.ice path models from the KPZ universality class: the directed random polymer with inverse-gamma weights (known as log-gamma polymer) and its zero temperature degeneration, i.e. the last passage percolation model, with geometric or exponential waiting times. We consider three path geometries: point-to-line, point-to-half-line, and point-to-line with paths restricted to stay in a half-plane. Through exact formulas, we establish new connections between integrable probabilistic models and the ubiquitous Whitaker and Schur functions.
More in detail, via the use of A. N. Kirillov’s geometric Robinson-Schensted-Knuth (RSK) correspondence, we compute the Laplace transform of the polymer partition functions in the above geometries in terms of orthogonal Whitaker functions. In the case of the first two geometries we also provide multiple contour integral formulas.
For the corresponding last passage percolation problems, we obtain new formulas in terms of symplectic Schur functions, both directly via RSK on polygonal arrays and via zero temperature limit from the log-gamma polymer formulas. As scaling limits of the point-toline and point-to-half-line models with exponential waiting times, we derive Sasamoto’s Fredholm determinant formula for the GOE Tracy-Widom distribution, as well as the one point marginal distribution of the Airy2-->1 process.
| Item Type: | Thesis (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Schur functions, Coulomb functions, Lattice paths, Laplace transformation, Polymers | ||||
| Official Date: | July 2018 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Department of Statistics | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Zygouras, Nikos | ||||
| Format of File: | |||||
| Extent: | xi, 128 leaves : illustrations | ||||
| Language: | eng |
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