(One-paragraph summary, 1998.)
Professor Rosenthal's research concerns probability theory and stochastic
processes. It focuses primarily on obtaining rigorous quantitative
bounds for rates of convergence for various Markov chains. Much of the
work concerns convergence of Markov chain Monte Carlo computational
algorithms such as the Gibbs Sampler, and includes general methods
(Rosenthal, JASA 1995; Baxter and Rosenthal, Stat. Prob. Lett. 1995;
Roberts and Rosenthal, Elec. J. Prob. 1996; Stoch. Models 1995),
detailed analysis of specific models (Rosenthal, Ann. Appl. Prob. 1993;
Ann. Stat. 1995; Stat. and Comp. 1996), theoretical results (Rosenthal,
Stoch. Proc. Appl. 1996; Roberts and Rosenthal, Stoch. Models 1997;
Elec. Comm. Prob. 1997; Ann. Appl. Prob. 1998; Roberts, Rosenthal,
and Schwartz, J. Appl. Prob. 1998) and bounds through auxiliary
simulation (Cowles and Rosenthal, Stat. and Comput. 1998).
Related work has focused on convergence of random walks on compact
groups including analysis of the ``cut-off phenomenon'' (Rosenthal,
Ann. Prob. 1994; J. Appl. Prob. 1993; Adv. Appl. Math. 1995), and
also on convergence of certain particle systems (Hoffman and Rosenthal,
Stoch. Proc. Appl. 1995).
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