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Informal Probability Workshop – Monday 5th February

05 Feb 18

Speaker:   Robin Stephenson, University of Oxford

Date:          Monday 5th February, 12 noon, The Mathematical Institute, Andrew Wiles Building, L5

Title:           Convergence of bivariate Markov chains to multi-type self-similar processes, and scaling limits of recursively growing trees.

Abstract:  We investigate the scaling limits of sequences of random trees obtained by recursive constructions. One crucial element is identifying their so-called Markov branching structure, which can be seen as a generalised Galton-Watson-type property, where individuals have mass and spread their mass to their children. The general study of Markov branching trees involves specific bivariate Markov chains, of which we then show the convergence to multi-type self-similar processes under various conditions.