Mathematics Commons^™

Matroid Generalizations Of Some Graph Results, Cameron Crenshaw

LSU Doctoral Dissertations

The edges of a graph have natural cyclic orderings. We investigate the matroids for which a similar cyclic ordering of the circuits is possible. A full characterization of the non-binary matroids with this property is given. Evidence of the difficulty of this problem for binary matroids is presented, along with a partial result for binary orderable matroids.

For a graph G, the ratio of |E(G)| to the minimum degree of G has a natural lower bound. For a matroid M that is representable over a finite field, we generalize this to a lower bound on …

Sl(2,Z) Representations And 2-Semiregular Modular Categories, Samuel Nathan Wilson

LSU Doctoral Dissertations

We address the open question of which representations of the modular group SL(2,Z) can be realized by a modular category. In order to investigate this problem, we introduce the concept of a symmetrizable representation of SL(2,Z) and show that this property is necessary for the representation to be realized. We then prove that all congruence representations of SL(2,Z) are symmetrizable. The proof involves constructing a symmetric basis, which greatly aids in further calculation. We apply this result to the reconstruction of modular category data from representations, as well as to the classification of semiregular categories, which are defined via an …

Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh

LSU Doctoral Dissertations

In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*-$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized Segal-Bargmann transform, where …

Modelling Illiquid Stocks Using Quantum Stochastic Calculus, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Symmetric Functions Algebras I: Introduction And Basic Features, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Random Variables With Overlapping Number And Weyl Algebras I, Ruma Dutta, Gabriela Popa, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Odds And Ends, Jimmie D. Lawson

Seminar on Continuity in Semilattices

No date.

Something, Gerhard Gierz

Seminar on Continuity in Semilattices

No date.

Pricing Multi-Asset Contingent Claims In A Multi-Dimensional Binomial Market, Jarek Kedra, Assaf Libman, Victoria Steblovskaya

Journal of Stochastic Analysis

No abstract provided.

The Malliavin-Stein Method For Normal Random Walks With Dependent Increments, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi

Journal of Stochastic Analysis

No abstract provided.

Runge-Kutta Methods For Rough Differential Equations, Martin Redmann, Sebastian Riedel

Journal of Stochastic Analysis

No abstract provided.

A Jump-Diffusion Process For Asset Price With Non-Independent Jumps, Yihren Wu, Majnu John

Journal of Stochastic Analysis

No abstract provided.

Quantization Of The Monotone Poisson Central Limit Theorem, Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Applications Of A Superposed Ornstein-Uhlenbeck Type Processes, Santatriniaina Avotra Randrianambinina, Julius Esunge

Journal of Stochastic Analysis

No abstract provided.

On The Diagonalizability And Factorizability Of Quadratic Boson Fields, Luigi Accardi, Andreas Boukas, Yungang Lu, Alexander Teretenkov

Journal of Stochastic Analysis

No abstract provided.

Fractal Like Snowflakes Generated By Non-Contractive Function Systems, William H. Kelly Iii

LSU Master's Theses

At the heart of this thesis is the examination of a non-contractive iterative function system T on the Hausdorff metric space of all compact subset of ℝ . Despite the absence of an 2 attracting fixed point, an examination reveals the appearance of fractal-like shapes (snowflakes) when applying the Barnsley’ random walk method to study the iterative sequence ��ⁿ(0) (�� ∈ ℕ) for �� = ��¹ ∪ ��² ∪ ��³, where ��₁(��) = ����, ��₂(��) = ���� + ��, and ��₃(��) = ���� - ��, and �� = …

The Degree Gini Index Of Several Classes Of Random Trees And Their Poissonized Counterparts—Evidence For Duality, Carly Domicolo, Panpan Zhang, Hosam Mahmoud

Journal of Stochastic Analysis

No abstract provided.

A Cluster Structure On The Coordinate Ring Of Partial Flag Varieties, Fayadh Kadhem

LSU Doctoral Dissertations

The main goal of this dissertation is to show that the (multi-homogeneous) coordinate ring of a partial flag variety C[G/P_K^−] contains a cluster algebra for every semisimple complex algebraic group G. We use derivation properties and a canonical lifting map to prove that the cluster algebra structure A of the coordinate ring C[N_K] of a Schubert cell constructed by Goodearl and Yakimov can be lifted, in an explicit way, to a cluster structure \hat{A} living in the coordinate ring of the corresponding partial flag variety. Then we use a minimality condition to prove that the cluster algebra \hat{A} is equal …

A Sharp Rate Of Convergence In The Functional Central Limit Theorem With Gaussian Input, S.V. Lototsky

Journal of Stochastic Analysis

No abstract provided.

Quantization Of The Free Poisson Central Limit Theorem, Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Quantization Of The Boolean Poisson Central Limit Theorem And A Generalized Boolean Bernoulli Sequence, Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

A First-Passage Problem For Exponential Integrated Diffusion Processes, Mario Lefebvre

Journal of Stochastic Analysis

No abstract provided.

Domain Of Exotic Laplacian Constructed By Wiener Integrals Of Exponential White Noise Distributions, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

The Construction And Estimation Of Hidden Semi-Markov Models, Kurdstan Abdullah, John Van Der Hoek

Journal of Stochastic Analysis

No abstract provided.

The Thermodynamics Of A Stochastic Geometry Model With Applications To Non-Extensive Statistics, O.K. Kazemi, A. Pourdarvish, J. Sadeghi

Journal of Stochastic Analysis

No abstract provided.

Quantization Of The Poisson Type Central Limit Theorem (1), Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

On A Relation Between Ado And Links-Gould Invariants, Nurdin Takenov

LSU Doctoral Dissertations

In this thesis we consider two knot invariants: Akutsu-Deguchi-Ohtsuki(ADO) invariant and Links-Gould invariant. They both are based on Reshetikhin-Turaev construction and as such share a lot of similarities. Moreover, they are both related to the Alexander polynomial and may be considered generalizations of it. By experimentation we found that for many knots, the third order ADO invariant is a specialization of the Links-Gould invariant. The main result of the thesis is a proof of this relation for a large class of knots, specifically closures of braids with five strands.

Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage

LSU Doctoral Dissertations

The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an essential role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Grudsky and Vasilevski showed in 2002 that radial Toeplitz operators on $\mathcal{F}(\mathbb{C})$ generate a commutative $C^*$-algebra $\mathcal{T}^G$, while Esmeral and Maximenko showed that $C^*$-algebra $\mathcal{T}^G$ is isometrically isomorphic to the $C^*$-algebra $C_{b,u}(\mathbb{N}_0,\rho_1)$. In this thesis, we extend the result to $k$-quasi-radial symbols acting on the Fock space $\mathcal{F}(\mathbb{C}^n)$. …

A Closed Form Formula For The Stochastic Exponential Of A Matrix-Valued Semimartingale, Peter Kern, Christian Müller

Journal of Stochastic Analysis

No abstract provided.

Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann

Journal of Stochastic Analysis

No abstract provided.