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János Komlós (born 23 May 1942, in
Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...
) is a Hungarian-American
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 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 ...
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 continuous f ...
. He has been a professor of
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
at
Rutgers University Rutgers University ( ), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of three campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's C ...
since 1988. He graduated from the
Eötvös Loránd University Eötvös Loránd University (, ELTE, also known as ''University of Budapest'') 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 ...
, then became a fellow at the Mathematical Institute of the
Hungarian Academy of Sciences The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...
. Between 1984–1988 he worked at the
University of California, San Diego The University of California, San Diego (UC San Diego in communications material, formerly and colloquially UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California, United States. Es ...
.


Notable results

* Komlós' theorem: 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 ( ), arithmetic average, or just the ''mean'' or ''average'' is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results fr ...
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 Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathema ...
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+...+ηn)/n → β a.s. * With
Miklós Ajtai Miklós Ajtai (born 2 July 1946) is a computer scientist at the IBM Almaden Research Center, United States. In 2003, he received the Knuth Prize for his numerous contributions to the field, including a classic sorting network algorithm (devel ...
and Endre Szemerédi he proved the ''ct''2/log ''t'' upper bound for the Ramsey number ''R''(3,''t''). The corresponding lower bound was established by Jeong Han Kim 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 In computer science, comparator networks are abstract devices built up of a fixed number of "wires", carrying values, and comparator modules that connect pairs of wires, swapping the values on the wires if they are not in a desired order. Such ne ...
. * 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 l ...
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 Endre Szemerédi 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 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 In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the ...
, 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 ...
. * Together with
Miklós Ajtai Miklós Ajtai (born 2 July 1946) is a computer scientist at the IBM Almaden Research Center, United States. In 2003, he received the Knuth Prize for his numerous contributions to the field, including a classic sorting network algorithm (devel ...
and
Gábor Tusnády Gábor (sometimes written Gabor) may refer to: * Gábor (given name) * Gabor (surname) * Gabor sisters, the three famous actresses, Eva, Magda and Zsa Zsa * Several scientific terms named after Dennis Gabor ** Gabor atom ** Gabor filter, a linear ...
he proved in 1984 the AKT optimal matching theorem.


Degrees, awards

Komlós received his Ph.D. in 1967 from
Eötvös Loránd University Eötvös Loránd University (, ELTE, also known as ''University of Budapest'') 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 ...
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 to A ...
. In 1975, he received the Alfréd Rényi Prize, a prize established for researchers of the Alfréd Rényi Institute of Mathematics. In 1998, he was elected as an external member to the
Hungarian Academy of Sciences The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...
.Rutgers Mathematics Department – Recent Faculty Honors
.


See also

*
Komlós–Major–Tusnády approximation In probability theory, the Komlós–Major–Tusnády approximation (also known as the KMT approximation, the KMT embedding, or the Hungarian embedding) refers to one of the two strong embedding theorems: 1) approximation of random walk by a standar ...


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