Browsing Mathematics by Title
Now showing items 50-69 of 188
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Eigenvalue fluctuations for random regular graphs
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are <italic>universal</italic>. We probe the edges of universality by studying ... -
Eigenvalue Fluctuations of Random Matrices beyond the Gaussian Universality Class
(2013-11-14)The goal of this thesis is to develop one of the threads of what is known in random matrix theory as universality, which essentially is that a large class of matrices generalizing the Gaussian matrices (certain Wigner ... -
An electrodynamic inverse problem in chiral media
(1998)We consider the inverse problem of determining the electromagnetic material parameters of a body from information obtainable only at the boundary of the body; such information comes in the form of a boundary map which we ... -
Elliptic Inverse Problems
Inverse problems arise in various areas of science and engineering including medical imaging, computer vision, geophysics, solid mechanics, astronomy, and so forth. A wide range of these problems involve elliptic operators. ... -
Epidemics on critical random graphs: limits and continuum descriptions
Understanding how diseases spread through populations is vital for mitigation efforts. For any disease at hand, the specifics of how a disease spreads through a community depends on many factors: how the disease is ... -
Essential spanning forests and electric networks in groups
(1997)Let $\Gamma$ be a Cayley graph of a finitely generated group G. Subgraphs which contain all vertices of $\Gamma ,$ have no cycles, and no finite connected components are called essential spanning forests. The set ${\cal ... -
Estimating Norms of Matrix Functions using Numerical Ranges
(2013-11-14)We study Crouzeix's conjecture: for any polynomial p and any square matrix A, the spectral norm of the matrix p(A) is at most double of the supremum norm of the polynomial p on the numerical range of the matrix A. -
Face Numbers of Polytopes, Posets, and Complexes
A key tool that combinatorialists use to study simplicial complexes and polytopes is the {\bf $f$-vector} (or face vector), which records the number of faces of each dimension. In order to better understand the face numbers, ... -
Factorization Homology for Embedded Submanifolds
In this thesis I will explore the theory of factorization homology including prerequisitematerial required to understand the definitions and structures used in the theory. I will beginwith a brief survey of some basic ... -
Finite-Difference Methods for Second-Order Wave Equations with Reduced Dispersion Errors
Finite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate ... -
Finite-Difference Methods for the Wave Equation with Reduced Dispersion Errors
(2013-04-17)A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finite-difference (FD) schemes in the joint time-space domain to reduce dispersion error. The key idea is that the true dispersion relation ... -
Flavors of the Fubini-Bruhat Order
Fubini words are generalized permutations, allowing for repeated letters, and theyare in one-to-one correspondence with ordered set partitions. Brendan Pawlowski and Brendon Rhoades extended permutation matrices to pattern ... -
Formal group laws and hypergraph colorings
This thesis demonstrates a connection between formal group laws and chromatic symmetric functions of hypergraphs, two seemingly unrelated topics in the theory of symmetric functions. A formal group law is a symmetric ... -
Four Problems in Probability and Optimization
(2014-02-24)This thesis studies bootstrap percolation, a problem in probability, as well as several topics in the application of sums of squares to combinatorial optimization. In the chapter on percolation, we bound the critical ... -
Gaps of saddle connection directions for some branched covers of tori
We compute the gap distribution of directions of saddle connections for two classes of translation surfaces. One class will be the translation surfaces arising from gluing two identical tori along a slit. These yield the ... -
Geodesic X-Ray Transform on Asymptotically Hyperbolic Manifolds
This dissertation contains work of the author and joint work with C. Robin Graham concerning the geodesic X-ray transform in the setting of asymptotically hyperbolic manifolds. It is divided into three self contained ... -
A Geometric Perspective on First-Passage Competition
(2013-04-17)We study the macroscopic geometry of first-passage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ... -
Geometry and algorithms for signal recovery: from convex duality to non-convex formulations
Structured signal recovery is a central task in a variety of scientific applications, and naturally leads to non-linear and non-convex optimization problems that present many interesting mathematical and algorithmic ... -
Geometry and Optimization of Relative Arbitrage
This thesis is devoted to the mathematics of volatility harvesting, the idea that extra portfolio growth may be created by systematic rebalancing. First developed by E. R. Fernholz in the late 90s and the early 2000s, ... -
Graded group schemes
We define graded group schemes and graded group varieties and develop their theory. We give a generalization of the result that connected graded bialgebras are graded Hopf algebra. Our result is given for a broader class ...