Arratia developed the ideas of interlace polynomials with Béla Bollobás and Gregory Sorkin,[paper 1] found an equivalent formulation of the Stanley–Wilf conjecture as the convergence of a limit,[paper 2] and was the first to investigate the lengths of superpatterns of permutations.[paper 2]
He has also written highly cited papers on the Chen–Stein method on distances between probability distributions,[paper 3][paper 4] on random walks with exclusion,[paper 5] and on sequence alignment.[paper 6][paper 7]
Education and employment
Arratia earned his Ph.D. in 1979 from the University of Wisconsin–Madison under the supervision of David Griffeath. He is currently a professor of mathematics at the University of Southern California.
- Research papers
- Arratia, Richard; Bollobás, Béla; Sorkin, Gregory B. (2004), "The interlace polynomial of a graph", Journal of Combinatorial Theory, Series B, 92 (2): 199–233, arXiv: , doi:10.1016/j.jctb.2004.03.003, MR 2099142.
- Arratia, Richard (1999), "On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern", Electronic Journal of Combinatorics, 6, N1, MR 1710623
- Arratia, R.; Goldstein, L.; Gordon, L. (1989), "Two moments suffice for Poisson approximations: the Chen–Stein method" (PDF), Annals of Probability, 17 (1): 9–25, JSTOR 2244193, MR 972770.
- Arratia, Richard; Goldstein, Larry; Gordon, Louis (1990), "Poisson approximation and the Chen–Stein method", Statistical Science, 5 (4): 403–434, doi:10.1214/ss/1177012015, JSTOR 2245366, MR 1092983.
- Arratia, Richard (1983), "The motion of a tagged particle in the simple symmetric exclusion system on Z", Annals of Probability, 11 (2): 362–373, JSTOR 2243693, MR 690134.
- Arratia, R.; Gordon, L.; Waterman, M. S. (1990), "The Erdős-Rényi law in distribution, for coin tossing and sequence matching" (PDF), Annals of Statistics, 18 (2): 539–570, doi:10.1214/aos/1176347615, MR 1056326.
- Arratia, Richard; Waterman, Michael S. (1994), "A phase transition for the score in matching random sequences allowing deletions" (PDF), Annals of Applied Probability, 4 (1): 200–225, doi:10.1214/aoap/1177005208, JSTOR 2245052, MR 1258181.
- Holst, Lars (2004), "Book Reviews: Logarithmic Combinatorial Structures: A Probabilistic Approach", Combinatorics, Probability and Computing, 13 (6): 916–917, doi:10.1017/S0963548304226566.
- Stark, Dudley (2005), "Book Reviews: Logarithmic Combinatorial Structures: A Probabilistic Approach", Bulletin of the London Mathematical Society, 37 (1): 157–158, doi:10.1112/S0024609304224092.
- Richard Arratia at the Mathematics Genealogy Project
- Faculty listing, USC Mathematics, retrieved 2013-06-01.
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