Mathematics - Ph.D. / Sc.D.
http://hdl.handle.net/1721.1/7843
Sat, 20 Jun 2015 07:18:43 GMT2015-06-20T07:18:43ZConformal loop ensembles and the Gaussian free field
http://hdl.handle.net/1721.1/97319
Conformal loop ensembles and the Gaussian free field
Watson, Samuel Stewart, 1986-
The study of two-dimensional statistical physics models leads naturally to the analysis of various conformally invariant mathematical objects, such as the Gaussian free field, the Schramm-Loewner evolution, and the conformal loop ensemble. Just as Brownian motion is a scaling limit of discrete random walks, these objects serve as universal scaling limits of functions or paths associated with the underlying discrete models. We establish a new convergence result for percolation, a well-studied discrete model. We also study random sets of points surrounded by exceptional numbers of conformal loop ensemble loops and establish the existence of a random generalized function describing the nesting of the conformal loop ensemble. Using this framework, we study the relationship between Gaussian free field extrema and nesting extrema of the ensemble of Gaussian free field level loops. Finally, we describe a coupling between the set of all Gaussian free field level loops and a conformal loop ensemble growth process introduced by Werner and Wu. We prove that the dynamics are determined by the conformal loop ensemble in this coupling, and we use this result to construct a conformally invariant metric space.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 173-178).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/1721.1/973192015-01-01T00:00:00ZAn Erlanger program for combinatorial geometries.
http://hdl.handle.net/1721.1/95532
An Erlanger program for combinatorial geometries.
Kung, Joseph Pee Sin
Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Bibliography: leaves 132-137.
Sun, 01 Jan 1978 00:00:00 GMThttp://hdl.handle.net/1721.1/955321978-01-01T00:00:00ZOn moduli stacks of finite group schemes
http://hdl.handle.net/1721.1/93003
On moduli stacks of finite group schemes
Zhang, Zhaohui, 1972-
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000.; Includes bibliographical references (p. 41-42).
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/1721.1/930032000-01-01T00:00:00ZWitt spaces : a geometric cycle theory for KO-homology at odd primes.
http://hdl.handle.net/1721.1/91309
Witt spaces : a geometric cycle theory for KO-homology at odd primes.
Siegel, Paul Howard
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979.; MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE.; Vita.; Bibliography: leaves 131-133.
Mon, 01 Jan 1979 00:00:00 GMThttp://hdl.handle.net/1721.1/913091979-01-01T00:00:00Z