János Komlós (mathematician)
Template:Short description Template:Western name order János Komlós (born 23 May 1942, in Budapest) is a Hungarian-American mathematician, working in probability theory and discrete mathematics. He has been a professor of mathematics at Rutgers University[1] since 1988. He graduated from the Eötvös Loránd University, then became a fellow at the Mathematical Institute of the Hungarian Academy of Sciences. Between 1984–1988 he worked at the University of California, San Diego.[2]
Notable results
- Komlós' theorem: He proved that every L1-bounded sequence of real functions contains a subsequence such that the arithmetic means of all its subsequences converge pointwise almost everywhere. In probabilistic terminology, the theorem is as follows. Let ξ1,ξ2,... be a sequence of random variables such that E[ξ1],E[ξ2],... 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 and Endre Szemerédi he proved[3] the ct2/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 same team of authors developed the optimal Ajtai–Komlós–Szemerédi sorting network.[4]
- Komlós and Szemerédi proved that if G is a random graph 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 graphs when considering the embedding of graphs with bounded degrees.[5]
- Komlós worked on Heilbronn's problem; he, János Pintz and Szemerédi disproved Heilbronn's conjecture.[6]
- Komlós also wrote highly cited papers on sums of random variables,[7] space-efficient representations of sparse sets,[8] random matrices,[9] the Szemerédi regularity lemma,[10] and derandomization.[11]
Degrees, awards
Komlós received his Ph.D. in 1967 from Eötvös Loránd University under the supervision of Alfréd Rényi.[12] 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.[13]
See also
References
- ↑ Template:Cite web
- ↑ UCSD Maths Dept history Template:Webarchive
- ↑ M. Ajtai, J. Komlós, E. Szemerédi: A note on Ramsey numbers, J. Combin. Theory Ser. A, 29(1980), 354–360.
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- ↑ J. Komlós, G. Sárközy, Szemerédi: Blow-Up Lemma, Combinatorica, 17(1997), 109–123.
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- ↑ Template:Citation. A preliminary version appeared in 23rd Symposium on Foundations of Computer Science, 1982, Template:Doi.
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- ↑ Rutgers Mathematics Department – Recent Faculty Honors Template:Webarchive.