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dc.contributor.advisorAlexei Borodin.en_US
dc.contributor.authorDimitrov, Evgeni (Evgeni Simeonov)en_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.date.accessioned2018-09-17T15:47:59Z
dc.date.available2018-09-17T15:47:59Z
dc.date.copyright2018en_US
dc.date.issued2018en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/117872
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.en_US
dc.descriptionCataloged from PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 235-239).en_US
dc.description.abstractWe present a collection of results about the scaling limits of several models from integrable probability. Our first result concerns the asymptotic behavior of the bottom slice of a Hall-Littlewood random plane partition. We show the latter concentrates around a limit shape and in two different scaling regimes identify the fluctuations around this shape with the GUE Tracy- Widom distribution and the narrow wedge initial data solution to the Kardar-Parisi-Zhang (KPZ) equation. The second result concerns the limiting behavior of a class of six-vertex models in the quadrant, and we obtain the GUE-corners process as a scaling limit for this class near the boundary. Our final result, joint with Ivan Corwin, demonstrates the (long predicted) transversal 2/3 critical exponent for the height functions of the stochastic sixvertex model and asymmetric simple exclusion process (ASEP). The algebraic parts of our arguments involve the construction and use of degenerations and modifications of the Macdonald difference operators to obtain rich families of observables for the models we consider. These formulas are in terms of multiple contour integrals and provide a direct access to quantities of interest. The analytic parts of our arguments include the detailed asymptotic analysis of Fredholm determinants and contour integrals through steepest descent methods. An important aspect of our approach, is the combination of exact formulas with more probabilistic arguments, based on various Gibbs properties enjoyed by the models we study.en_US
dc.description.statementofresponsibilityby Evgeni Dimitrov.en_US
dc.format.extent239 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectMathematics.en_US
dc.titleScaling limits of random plane partitions and six-vertex modelsen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematics.en_US
dc.identifier.oclc1051190327en_US


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