Richard Arratia

Richard Arratia is a Professor of Mathematics at the University of Southern California, affiliated with the College of Letters, Arts and Sciences and the Center for Applied Mathematical Sciences. His research focuses on discrete probability, combinatorics, and number theory, particularly the interplay between dependence and independence in probabilistic systems.

• Education: B.S. from Massachusetts Institute of Technology, Ph.D. from University of Wisconsin, Madison.

His work explores approximations of probabilities for rare events, continuum limits of discrete systems (e.g., coalescing Brownian motions), and logarithmic combinatorial structures such as permutations with cycle decompositions and prime factorizations of integers. He has co-authored a foundational book on logarithmic combinatorial structures and published extensively on topics including Poisson approximation, random walks, symmetric exclusion processes, and interlace polynomials for graphs.

His recent publications highlight applications of probabilistic methods to integer partitions, graph theory, and statistical analysis. Key themes include exact simulation techniques, graphical sequences, and connections between analytic number theory and probabilistic models.

Professor Arratia serves as faculty advisor to Pi Mu Epsilon, the undergraduate mathematics honors society, and has contributed to research in probability asymptotics, logistic regression, and algebraic function fields.