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I have been interested in interfaces between the traditional theory of stochastic processes and other areas of mathematics, especially combinatorics. I have studied various random combinatorial objects, such as permutations, partitions, and trees, and how the asymptotic behaviour of such structures over a large number of elements can be described in probabilistic terms, most often involving Brownian motion and related processes. This has led to the study of various measure-valued and partition-valued Markov processes whose behaviour may be understood in terms of combinatorial constructions involving random trees. I am at present engaged in developing various ideas related to random partitions, random trees, irreversible processes of coalescence, and their time reversals which provide models for random splitting or fragmentation.
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COMBINATORICS PROBABILITY & COMPUTINGno. 2 (2023): 1-28
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