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János Komlós (Budapest, 23 May 1942) is a Hungarian-American mathematician, working in probability theory and discrete mathematics. He has been a professor of mathematics at Rutgers University〔(Rutgers faculty profile for Komlós ).〕 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 at San Diego.〔(UCSD Maths Dept history )〕 ==Notable results== * 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''(),''E''(),... 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 Ajtai and Szemerédi he proved〔M. Ajtai, J. Komlós, E. Szemerédi: A note on Ramsey numbers, ''J. Combin. Theory Ser. A'', 29(1980), 354–360.〕 the ''ct''2/log ''t'' upper bound for the Ramsey number ''R''(3,''t''). The corresponding lower bound was proved by Kim only in 1995, this result earned him a Fulkerson Prize. * The same team of authors developed the optimal Ajtai–Komlós–Szemerédi sorting network.〔; .〕 * 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.〔J. Komlós, G. Sárközy, Szemerédi: Blow-Up Lemma, ''Combinatorica'', 17(1997), 109–123.〕 * 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,〔. A preliminary version appeared in 23rd Symposium on Foundations of Computer Science, 1982, .〕 random matrices,〔.〕 the Szemerédi regularity lemma,〔.〕 and derandomization.〔.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「János Komlós (mathematician)」の詳細全文を読む スポンサード リンク
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