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A multi-layer extension of the stochastic heat equation
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Lun, Chin Hang (2016) A multi-layer extension of the stochastic heat equation. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2867107~S1
Abstract
The KPZ universality class is expected to contain a large class of random growth processes. In some of these models, there is an additional structure provided by multiple non-intersecting paths and utilisation of this additional structure has led to derivations of exact formulae for the distribution of quantities of interest. Motivated by this we study the multi-layer extension of the stochastic heat equation introduced by O'Connell and Warren in [OW11] which is the continuum analogue of the above mentioned structure. We also show that a multi-layer Cole-Hopf solution to the KPZ equation is well defined.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Heat equation | ||||
Official Date: | March 2016 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Warren, Jon ; Tribe, Roger | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) (EP/H023364/1) | ||||
Extent: | v, 111 leaves | ||||
Language: | eng |
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