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05/06/04 Colloquium
DR. KEITH HOPCRAFT
SCHOOL OF MATHEMATICAL SCIENCES
UNIVERSITY OF NOTTINGHAM
SCHOOL OF MATHEMATICAL SCIENCES
UNIVERSITY OF NOTTINGHAM
Generation and Modelling of Discrete Stable Random Processes Using Population Models
Abstract: Intermittent pulse-like behavior can be observed in a variety of physical systems, such as the Edge Localised Modes (ELMS) in magnetically confined plasmas, temperature fluctuations observed in the Sorret effect, and caustics generated by light propagating through a phase screen. Discrete random variables with fractal characteristics have recently been shown to describe the topology of the WWW and other complex networks, and provide a motor for some of the intermittent behaviors exhibited by sandpiles. Modelling such effects using continuum field theories provides significant challenges because of the disparate time and/or spatial scales involved. An alternative approach is to develop stochastic models of discrete random variables that encapsulate the pulse-like phenomenology observed in these disparate systems. The talk will consider the discrete analogue of the continuous Levy-stable class of distributions and discuss some of their properties. It will then be shown how these distributions can be generated from simple stochastic population models that are a generalization of well-known birth-death-immigration processes.