Exact and asymptotic solutions of the call auction problem

The call auction is a widely used trading mechanism, especially during the opening and closing periods of financial markets. In this paper, we study a standard call auction problem where orders are submitted according to Poisson processes, with random prices distributed according to a general distribution, and may be cancelled at any time. We compute the analytical expressions of the distributions of the traded volume, of the lower and upper bounds of the clearing prices, and of the price range of these possible clearing prices of the call auction. Using results from the theory of order statistics and a theorem on the limit of sequences of random variables with independent random indices, we derive the weak limits of all these distributions. In this setting, traded volume and bounds of the clearing prices are found to be asymptotically normal, while the clearing price range is asymptotically exponential. All the parameters of these distributions are explicitly derived as functions of the parameters of the incoming orders' flows.Comment: 24 pages, 7 figure

Scalar Perturbations of two-dimensional Horava-Lifshitz Black Holes

In this article, we study the stability of black hole solutions found in the context of dilatonic Horava-Lifshitz gravity in $1+1$ dimensions by means of the quasinormal modes approach. In order to find the corresponding quasinormal modes, we consider the perturbations of massive and massless scalar fields minimally coupled to gravity. In both cases, we found that the quasinormal modes have a discrete spectrum and are completely imaginary, which leads to damping modes. For a massive scalar field and a non-vanishing cosmological constant, our results suggest unstable behaviour for large values of the scalar field mass.Comment: 18 pages, 1 figure. Accepted version in EPJC. arXiv admin note: text overlap with arXiv:gr-qc/070109

Enhancement of the magnetic moment of the electron due to a topological defect

In the framework of the theory of defects/three-dimensional gravitation, it is obtained a positive correction to the magnetic moment of the electron bound to a disclination in a dielectric solid.Comment: LaTeX twice, 5 page

The Role of Continuum States in the Field Ionization of Rydberg Atoms

In an experiment performed by our collaborators at Bryn Mawr, we excite rubidium-85 to a coherent superposition of the different |mj| splittings of the 37d5/2 state induced by a small electric field. After waiting for some variable delay time, we apply a time-dependent electric field to ionize the atom and record the ionized current that arrives at the detector. Due to the initial superposition, we observe an interference pattern that depends on the delay time. This thesis describes my continued work with Dr. Carroll to develop a computational model of this experiment. Our initial method of determining the current involved a semi-classical approach that did not accurately describe the phase, so the more recent developments have focused on including the continuum states in our calculation