Professor James Norris
Email address: J.R.Norris[at]statslab.cam.ac.uk
Telephone: 01223 (3)37947
Research interests: Topics in probability and analysis, including stochastic differential equations, Malliavin calculus, analysis of heat kernels, homogenization, Brownian motion and Brownian sheet, stochastic differential geometry, models of coagulation and coalescence.
Let me describe in a little more detail my interest in coagulation. In diverse contexts one is led to consider a large system of particles (bubbles, droplets, stars, molecules...) which, over time, stick together to form larger particles. This can be modelled as a Markov random process. The challenge is to discover the possible sorts of behaviour of these systems: is there a non-random approximation giving the evolving concentrations of particles of various masses, do most of the particles eventually (or instantaneously) stick together, do spatial fluctuations matter, does the mass distribution, suitably renormalised, converge in long time? These are questions of interest to scientists in many fields but a rigorous mathematical theory has only partly emerged. Techniques relevant to the analysis of these processes are martingales, weak convergence, coupling of processes and plenty of careful estimates.
Further details can be found on my Personal Home Page.
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