Mathematical Sciences: Probabilistic Aspects of Trees with Applications to Manifolds and Groups

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This research involves the study of random processes on trees. In particular, for random walks on random trees, problems to be studied include the speed of the walks and the Hausdorff dimension of their harmonic measure. These questions are analogous to current investigations in differential geometry. Another problem is to approximate negatively curved manifolds by trees in order to study some random processes on manifolds. This research involves the study of random processes on trees. Trees are structures that are often more realistic than Euclidean spaces as models for movement of random processes. This research will contribute to a better understanding of random processes.