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Extremal and probabilistic bootstrap percolation
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-11-12)
In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest ...
Maximum likelihood parameter estimation in time series models using sequential Monte Carlo
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryDarwin College, 2013-06-11)
Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...
Automorphisms of free products of groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2013-02-05)
The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ...
Chaos and Entropic Chaos in Kac's Model Without High Moments
(Institute of Mathematical StatisticsElectronic Journal of Probability, 2013-08-27)
In this paper we present a new local Lévy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying ...