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Full-Text Articles in Mathematics
A Brascamp-Lieb–Rary Of Examples, Anina Peersen
A Brascamp-Lieb–Rary Of Examples, Anina Peersen
Mathematics, Statistics, and Computer Science Honors Projects
This paper focuses on the Brascamp-Lieb inequality and its applications in analysis, fractal geometry, computer science, and more. It provides a beginner-level introduction to the Brascamp-Lieb inequality alongside re- lated inequalities in analysis and explores specific cases of extremizable, simple, and equivalent Brascamp-Lieb data. Connections to computer sci- ence and geometric measure theory are introduced and explained. Finally, the Brascamp-Lieb constant is calculated for a chosen family of linear maps.
Mixing Measures For Trees Of Fixed Diameter, Ari Holcombe Pomerance
Mixing Measures For Trees Of Fixed Diameter, Ari Holcombe Pomerance
Mathematics, Statistics, and Computer Science Honors Projects
A mixing measure is the expected length of a random walk in a graph given a set of starting and stopping conditions. We determine the tree structures of order n with diameter d that minimize and maximize for a few mixing measures. We show that the maximizing tree is usually a broom graph or a double broom graph and that the minimizing tree is usually a seesaw graph or a double seesaw graph.