János Komlós (mathematician)
János Komlós (born 23 May 1942, in
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
- 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 circuitconverges to
- With 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,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
- ^ [1].
- ^ UCSD Maths Dept history Archived 2008-10-28 at the Wayback Machine
- ^ M. Ajtai, J. Komlós, E. Szemerédi: A note on Ramsey numbers, J. Combin. Theory Ser. A, 29(1980), 354–360.
- S2CID 519246.
- ^ J. Komlós, G. Sárközy, Szemerédi: Blow-Up Lemma, Combinatorica, 17(1997), 109–123.
- S2CID 8272486.
- .
- S2CID 7847476.
- ^ Komlós, János; Simonovits, Miklós (1996), Szemeredi's Regularity Lemma and its applications in graph theory, Technical Report: 96-10, DIMACS.
- S2CID 15323404.
- ^ János Komlós at the Mathematics Genealogy Project.
- ^ Rutgers Mathematics Department – Recent Faculty Honors Archived 2008-12-18 at the Wayback Machine.