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A Random Hierarchical Laplacian
Title
A Random Hierarchical Laplacian
Author
Ray, Elijah
Date Created
2013
Subjects--Topical
Mathematics
Description
The Hierarchical Laplacian, proposed in Dyson's theory of one-dimensional ferromagnetic phase transitions, has a discrete spectrum with each isolated eigenvalue having infinite multiplicity. As a result, the integrated density of states is piecewi...
Intermittency for Branching random walks with heavy tails.
Title
Intermittency for Branching random walks with heavy tails.
Author
Getan, Asmaa
Date Created
2016
Subjects--Topical
Mathematics
Description
iic 2016Asmaa GetanALL RIGHTS RESERVEDiiiABSTRACT Branching Markov process models populations in which each individual in gener-ation n produces some random number of individuals in the next generation, n + 1, according to a certain probability di...
ON THE DISCRETE SPECTRUM OF EXTERIOR ELLIPTIC PROBLEMS.
Title
ON THE DISCRETE SPECTRUM OF EXTERIOR ELLIPTIC PROBLEMS.
Author
Puri, Rajan
Date Created
2019
Subjects--Topical
Mathematics
Description
In this dissertation, we present three new results in the exterior elliptic problems with the variable coefficients that describe the process in inhomogeneous media in the presence of obstacles. These results concern perturbations of the operator ...
On the spectral theory of 1-D Schrodinger operator with random sparse potentials
Title
On the spectral theory of 1-D Schrodinger operator with random sparse potentials
Author
Cook, Thomas
Date Created
2019
Subjects--Topical
Mathematics
Description
The goal of this dissertation is to develop a spectral theory for the Schr\"odinger operator with sparse random potential. To do this, we will first reformulate theories for sparse deterministic potentials. This includes a general development of t...
Spectral Theory of Schrödinger Type Operator on Spider Type Quantum Graphs
Title
Spectral Theory of Schrödinger Type Operator on Spider Type Quantum Graphs
Author
Paul, Madhumita
Date Created
2023
Subjects--Topical
Mathematics
Description
The dissertation consists of chapter 1: Introduction, this chapter contains some definitions and examples of quantum graphs, symplectic analysis and its representation on spider graph. Chapter 2-Brownian motion on the spider like quantum graph, th...
Spectral theory of the Schrodinger operator on general graphs
Title
Spectral theory of the Schrodinger operator on general graphs
Author
Zheng, Lukun
Date Created
2015
Subjects--Topical
Mathematics, Physics
Description
The goal of this dissertation is to give the sufficient conditions for the absence of a.c.spectrum or existence of the pure point (p.p.) spectrum for the deterministic or random Schrodinger operators on the general graphs. For the particular situa...