Richard Alejandro Arratia is a mathematician noted for his work in
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
and
probability theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...
.
Contributions
Arratia developed the ideas of
interlace polynomials with
Béla Bollobás
Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul E ...
and Gregory Sorkin,
[.] found an equivalent formulation of the
Stanley–Wilf conjecture
The Stanley–Wilf conjecture, formulated independently by Richard P. Stanley and Herbert Wilf in the late 1980s, states that the growth rate of every proper permutation class is Exponential growth, singly exponential. It was proved by and is no l ...
as the convergence of a limit,
and was the first to investigate the lengths of
superpattern In the mathematical study of permutations and permutation patterns, a superpattern or universal permutation is a permutation that contains all of the patterns of a given length. More specifically, a ''k''-superpattern contains all possible patterns ...
s of permutations.
He has also written highly cited papers on the
Chen–Stein method on distances between
probability distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...
s,
[.][.] on
random walk
In mathematics, a random walk, sometimes known as a drunkard's walk, is a stochastic process that describes a path that consists of a succession of random steps on some Space (mathematics), mathematical space.
An elementary example of a rand ...
s with exclusion,
[.] and on
sequence alignment
In bioinformatics, a sequence alignment is a way of arranging the sequences of DNA, RNA, or protein to identify regions of similarity that may be a consequence of functional, structural biology, structural, or evolutionary relationships between ...
.
[.][.]
He is a coauthor of the book ''Logarithmic Combinatorial Structures: A Probabilistic Approach''.
[.]
Education and employment
Arratia earned his Ph.D. in 1979 from the
University of Wisconsin–Madison
The University of Wisconsin–Madison (University of Wisconsin, Wisconsin, UW, UW–Madison, or simply Madison) is a public land-grant research university in Madison, Wisconsin, United States. It was founded in 1848 when Wisconsin achieved st ...
under the supervision of David Griffeath. He is currently a professor of mathematics at the
University of Southern California
The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...
.
Faculty listing
USC Mathematics, retrieved 2013-06-01.
Selected publications
;Research papers
;Books
References
External links
*
USC faculty page
{{DEFAULTSORT:Arratia, Richard Alejandro
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Combinatorialists
American probability theorists
Stuyvesant High School alumni
University of Wisconsin–Madison alumni
University of Southern California faculty