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High points of a Gaussian free field and a Gaussian membrane model and limit shape of Young diagrams for random permutations


Cipriani, Alessandra. High points of a Gaussian free field and a Gaussian membrane model and limit shape of Young diagrams for random permutations. 2014, University of Zurich, Faculty of Science.

Abstract

This thesis consists of two distinct parts. In the first part, we treat two different models of Gaussian Fields: one is the membrane model at its critical dimension, of which we establish the Hausdorff dimension of its high points, and the other one is the continuum Gaussian Free Field in dimension 4, of which we determine the Hausdorff dimension of the thick points and prove they constitute the support of the 4-dimensional Liouville Quantum Gravity measure. In the second part, we deal with random permutations and show the limit shape for Young diagrams under a so-called conservative measure on the set of permutations on n objects.

This thesis consists of two distinct parts. In the first part, we treat two different models of Gaussian Fields: one is the membrane model at its critical dimension, of which we establish the Hausdorff dimension of its high points, and the other one is the continuum Gaussian Free Field in dimension 4, of which we determine the Hausdorff dimension of the thick points and prove they constitute the support of the 4-dimensional Liouville Quantum Gravity measure. In the second part, we deal with random permutations and show the limit shape for Young diagrams under a so-called conservative measure on the set of permutations on n objects.

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Additional indexing

Item Type:Dissertation
Referees:Bolthausen Erwin, Nikeghbali Ashkan, Ueltschi Daniel
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2014
Deposited On:04 Mar 2015 11:34
Last Modified:05 Apr 2016 19:07
Number of Pages:112
Related URLs:http://opac.nebis.ch/F?func=direct&local_base=NEBIS&doc_number=010259016 (Library Catalogue)
Permanent URL: https://doi.org/10.5167/uzh-109240

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