(One-paragraph summary, 2002.)
Professor Rosenthal's research concerns probability theory and stochastic
processes. Much of it has involved obtaining rigorous quantitative
bounds for rates of convergence for various Markov chains, especially
Markov chain Monte Carlo computer algorithms such as the Gibbs Sampler.
It has included general methods, detailed analysis of specific models,
theoretical results, new coupling constructions, and convergence bounds
using auxiliary simulation. Related work has focused on convergence
of random walks on compact groups and the ``cut-off phenomenon'', on
convergence of certain particle systems, on link structures of the World
Wide Web, on applications to Economics and Finance, and on computational
data-analysis and data mining methods.
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