János Komlós (born 23 May 1942, in

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

) is a

Hungarian-American Hungarian Americans ( Hungarian: ''amerikai magyarok'') are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people wit ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, working in

probability theory Probability theory 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 expressing it through a set o ...

and

discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continu ...

. He has been a professor of mathematics at

Rutgers University Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and wa ...

since 1988. He graduated from the

Eötvös Loránd University Eötvös Loránd University ( hu, Eötvös Loránd Tudományegyetem, ELTE) is a Hungarian public research university based in Budapest. Founded in 1635, ELTE is one of the largest and most prestigious public higher education institutions in Hung ...

, then became a fellow at the Mathematical Institute of the

Hungarian Academy of Sciences The Hungarian Academy of Sciences ( hu, Magyar Tudományos Akadémia, MTA) is the most important and prestigious learned society of Hungary. Its seat is at the bank of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. Its mai ...

. Between 1984–1988 he worked at the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...

Notable results

* He proved that every L¹-bounded sequence of real functions contains a subsequence such that the

arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the '' average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The coll ...

s of all its subsequences converge pointwise almost everywhere. In probabilistic terminology, the theorem is as follows. Let ξ₁,ξ₂,... be a sequence of

random variable A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the p ...

s such that ''E'' �₁''E'' �₂... is bounded. Then there exist a subsequence ξ'₁, ξ'₂,... and a random variable β such that for each further subsequence η₁,η₂,... of ξ'₀, ξ'₁,... we have (η₁+...+η_n)/n → β a.s. * With Miklós Ajtai and

Endre Szemerédi Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science a ...

he proved the ''ct''²/log ''t'' upper bound for the

Ramsey number In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (s ...

''R''(3,''t''). The corresponding lower bound was established by

Jeong Han Kim Jeong Han Kim (; born July 20, 1962) is a South Korean mathematician. He studied physics and mathematical physics at Yonsei University, and earned his Ph.D. in mathematics at Rutgers University. He was a researcher at AT&T Bell Labs and at Micr ...

only in 1995, and this result earned him a

Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...

. * The same team of authors developed the optimal Ajtai–Komlós–Szemerédi sorting network. * Komlós and Szemerédi proved that if ''G'' is a

random graph In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs ...

on ''n'' vertices with :edges, where ''c'' is a fixed real number, then the probability that ''G'' has a Hamiltonian circuit converges to * With Gábor Sárközy and

he proved the so-called blow-up lemma which claims that the regular pairs in Szemerédi's regularity lemma are similar to

complete bipartite graph In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set..Electronic edition page 17. Graph theory ...

s when considering the embedding of graphs with bounded degrees. * Komlós worked on Heilbronn's problem; he,

János Pintz János Pintz (born 20 December 1950 in Budapest) is a Hungarian mathematician working in analytic number theory. He is a fellow of the Rényi Mathematical Institute and is also a member of the Hungarian Academy of Sciences. In 2014, he received ...

and Szemerédi disproved Heilbronn's conjecture. * Komlós also wrote highly cited papers on sums of random variables, space-efficient representations of sparse sets, random matrices, the Szemerédi regularity lemma, and

derandomization A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performan ...

Degrees, awards

Komlós received his Ph.D. in 1967 from

under the supervision of

Alfréd Rényi Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician known for his work in probability theory, though he also made contributions in combinatorics, graph theory, and number theory. Life Rényi was born in Budapest ...

. In 1975 he received the

Alfréd Rényi Prize The Alfréd Rényi Prize is awarded biennially by the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Science in honor of founder Alfréd Rényi. By the current rules it is given to one or two fellows of the Institute in recogni ...

, a prize established for researchers of the

Alfréd Rényi Institute of Mathematics The Alfréd Rényi Institute of Mathematics ( hu, Rényi Alfréd Matematikai Kutatóintézet) is the research institute in mathematics of the Hungarian Academy of Sciences. It was created in 1950 by Alfréd Rényi, who directed it until his death. ...

. In 1998 he was elected as an external member to the

.Rutgers Mathematics Department – Recent Faculty Honors
.

References

{{DEFAULTSORT:Komlos, Janos 1942 births Living people 20th-century Hungarian mathematicians 21st-century Hungarian mathematicians Members of the Hungarian Academy of Sciences Theoretical computer scientists Eötvös Loránd University alumni Rutgers University faculty

Notable results

Degrees, awards

See also

References