Convergence of Gibbs measures and the behavior of shrinking tubular neighborhoods of fractals and algebraic sets

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dc.contributor.advisorHardt, Robert M.en_US
dc.creatorSamansky, Eric Michaelen_US
dc.date.accessioned2009-06-03T21:08:13Zen_US
dc.date.available2009-06-03T21:08:13Zen_US
dc.date.issued2007en_US
dc.description.abstractAnnealing is a physical process that motivates our definition of a Gibbs measure, which is a certain probability measure on Euclidean space. In this paper we examine a sequence of Gibbs measures characterized by the distance function. In Chapter 2 we conclude that the sequence of measures converge to a Hausdorff probability measure equally distributed along self-similar fractals with Hutchinson's Open Set Condition. In Chapter 3 we study spaces of concentric circles (which we call targets) in the plane, and examine how the sequence of probability measures distributes over the targets. By varying the number of targets and the size of the circles, we find probability measures that divide their mass between different point masses and spaces. Finally, in Chapter 4 we conclude that the measure will distribute evenly over the highest-dimensional strata of any semi-algebraic set.en_US
dc.format.extent54 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH. 2007 SAMANSKYen_US
dc.identifier.citationSamansky, Eric Michael. "Convergence of Gibbs measures and the behavior of shrinking tubular neighborhoods of fractals and algebraic sets." (2007) Diss., Rice University. <a href="https://hdl.handle.net/1911/20643">https://hdl.handle.net/1911/20643</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/20643en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleConvergence of Gibbs measures and the behavior of shrinking tubular neighborhoods of fractals and algebraic setsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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