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1	A random matrix model for two-colour QCD at non-zero quark density Phillips, Michael James January 2011 (has links) We solve a random matrix ensemble called the chiral Ginibre orthogonal ensemble, or chGinOE. This non-Hermitian ensemble has applications to modelling particular low-energy limits of two-colour quantum chromo-dynamics (QCD). In particular, the matrices model the Dirac operator for quarks in the presence of a gluon gauge field of fixed topology, with an arbitrary number of flavours of virtual quarks and a non-zero quark chemical potential. We derive the joint probability density function (JPDF) of eigenvalues for this ensemble for finite matrix size N, which we then write in a factorised form. We then present two different methods for determining the correlation functions, resulting in compact expressions involving Pfaffians containing the associated kernel. We determine the microscopic large-N limits at strong and weak non-Hermiticity (required for physical applications) for both the real and complex eigenvalue densities. Various other properties of the ensemble are also investigated, including the skew-orthogonal polynomials and the fraction of eigenvalues that are real. A number of the techniques that we develop have more general applicability within random matrix theory, some of which we also explore in this thesis. 519
2	Empirical evaluation of a Markovian model in a limit order market Trönnberg, Filip January 2012 (has links) A stochastic model for the dynamics of a limit order book is evaluated and tested on empirical data. Arrival of limit, market and cancellation orders are described in terms of a Markovian queuing system with exponentially distributed occurrences. In this model, several key quantities can be analytically calculated, such as the distribution of times between price moves, price volatility and the probability of an upward price move, all conditional on the state of the order book. We show that the exponential distribution poorly fits the occurrences of order book events and further show that little resemblance exists between the analytical formulas in this model and the empirical data. The log-normal and Weibull distribution are suggested as replacements as they appear to fit the empirical data better. Markovian model limit order book limit order market stock stock market price dynamics log-normal distribution exponential Weibull Markovian queuing system empirical data financial assets trading trader high frequency trading order book order flow HFT Joint probability density function bid queue ask queue

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A random matrix model for two-colour QCD at non-zero quark density

Empirical evaluation of a Markovian model in a limit order market