# Browse Dissertations and Theses - Mathematics by Contributor "Kirkpatrick, Kay"

• (2017-04-07)
In the first part of this thesis, we will discuss the classical XY model on complete graph in the mean-field (infinite-vertex) limit. Using theory of large deviations and Stein's method, in particular, Cramér and Sanov-type ...

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• (2016-07-14)
In this dissertation, we will focus on a few problems in extremal graph theory. The first chapter consists of some basic terms and tools. In Chapter 2, we study a conjecture of Mader on embedding subdivisions of cliques. ...

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• (2017-04-19)
The fast developing field of extremal combinatorics provides a diverse spectrum of powerful tools with many applications to economics, computer science, and optimization theory. In this thesis, we focus on counting and ...

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• (2014-09-16)
Let $(\mathcal{N},\tau)$ be a noncommutative $W^*$ probability space, where $\mathcal{N}$ is a finite von Neumann algebra and $\tau$ is a normal faithful tracial state. Let $(T_t)_{\ge 0}$ be a normal, unital, completely ...

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• (2018-12-06)
Statistical physics, as a branch of modern physics, uses methods of probability theory and statistics to solve physical problems with large populations and approximations. In this thesis, we use numerical simulations to ...

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• (2017-04-19)
In this work we are interested in the stability bifurcations of the dynamical systems defined on graphs, and we use signed graph Laplacians as our tool. In chapter 1, we give the formal definition of the Laplacian matrix ...

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• (2017-04-05)
A classical problem in combinatorics is, given graphs G and H, to determine if H is a subgraph of G. It is usually computationally complex to determine if H is a subgraph of G. Therefore, we often prove conditions that ...

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• (2017-03-27)
This thesis focuses on using techniques from probability to solve problems from extremal and structural combinatorics. The main problem in Chapter 2 is determining the typical structure of $t$-intersecting families in ...

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