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| '''János Komlós''' ([[Budapest]], 23 May 1942) is a [[Hungarian American|Hungarian-American]] mathematician, working in [[probability theory]] and [[discrete mathematics]]. He is a professor of mathematics at [[Rutgers University]]<ref>[http://www.math.rutgers.edu/people/?type=faculty&id=199 Rutgers faculty profile for Komlós].</ref> since 1988. He graduated from the [[Eötvös Loránd University]], then became a fellow at the [[Alfréd Rényi Institute of Mathematics|Mathematical Institute]] of the [[Hungarian Academy of Sciences]]. Between 1984–1988 he worked at the [[University of California at San Diego]].<ref>[http://math.ucsd.edu/about/history/ UCSD Maths Dept history]</ref> | | I'm Vickey (31) from Laugarvatn, Iceland. <br>I'm learning Spanish literature at a local college and I'm just about to graduate.<br>I have a part time job in a post office.<br><br>my webpage ... [http://tinyurl.com/pch83be cheap ugg boots] |
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| ==Notable results==
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| * He proved that every [[L1 norm|L<sup>1</sup>]]-bounded sequence of real functions contains a subsequence such that the [[arithmetic mean]]s of all its subsequences [[Almost everywhere convergence|converge pointwise almost everywhere]]. In probabilistic terminology, the theorem is as follows. Let ξ<sub>1</sub>,ξ<sub>2</sub>,... be a sequence of [[random variable]]s such that ''E''[ξ<sub>1</sub>],''E''[ξ<sub>2</sub>],... is bounded. Then there exist a subsequence ξ'<sub>1</sub>, ξ'<sub>2</sub>,... and a random variable β such that for each further subsequence η<sub>1</sub>,η<sub>2</sub>,... of ξ'<sub>0</sub>, ξ'<sub>1</sub>,... we have (η<sub>1</sub>+...+η<sub>n</sub>)/n → β [[almost surely|a.s]].
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| * With [[Miklós Ajtai|Ajtai]] and [[Endre Szemerédi|Szemerédi]] he proved<ref>M. Ajtai, J. Komlós, E. Szemerédi: A note on Ramsey numbers,
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| ''J. Combin. Theory Ser. A'', '''29'''(1980), 354–360.</ref> the ''ct''<sup>2</sup>/log ''t'' upper bound for the [[Ramsey's_theorem#Ramsey_numbers|Ramsey number]] ''R''(3,''t''). The corresponding lower bound was proved by [[Jeong Han Kim|Kim]] only in 1995, this result earned him a [[Fulkerson Prize]].
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| * The same team of authors developed the optimal Ajtai–Komlós–Szemerédi [[sorting network]].<ref>{{citation|first1=Miklós|last1=Ajtai|author1-link=Miklós Ajtai|first2=János|last2=Komlós|first3=Endre|last3=Szemerédi|author3-link=Endre Szemerédi|contribution=An O(''n'' log ''n'') sorting network|title=[[Symposium on Theory of Computing|Proc. 15th ACM Symposium on Theory of Computing]]|year=1983|pages=1–9|doi=10.1145/800061.808726}}; {{citation|first1=Miklós|last1=Ajtai|author1-link=Miklós Ajtai|first2=János|last2=Komlós|first3=Endre|last3=Szemerédi|author3-link=Endre Szemerédi|title=Sorting in ''c'' log ''n'' parallel steps|journal=Combinatorica|volume=3|issue=1|year=1983|pages=1–19|doi=10.1007/BF02579338}}.</ref>
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| * Komlós and [[Endre Szemerédi|Szemerédi]] proved that if ''G'' is a [[random graph]] on ''n'' vertices with
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| <center><math>\frac12n\log n+\frac12n\log\log n+cn</math></center>
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| :edges, where ''c'' is a fixed real number, then the probability that ''G'' has a [[Hamiltonian circuit]] converges to
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| <center><math>e^{-e^{-2c}}.</math></center>
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| * With [[Gábor N. Sárközy|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]]s when considering the embedding of graphs with bounded degrees.<ref>J. Komlós, G. Sárközy, Szemerédi: Blow-Up Lemma, ''[[Combinatorica]]'', '''17'''(1997), 109–123.</ref>
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| * Komlós also wrote highly cited papers on sums of random variables,<ref>{{citation|title= An approximation of partial sums of independent RV'-s, and the sample DF. I|journal=Probability Theory and Related Fields|volume=32|issue=1–2|year=1975|doi=10.1007/BF00533093|pages=111–131|first1=J.|last1=Komlós|first2=P.|last2=Major|first3=G.|last3=Tusnády}}.</ref> space-efficient representations of sparse sets,<ref>{{citation|title=Storing a Sparse Table with O(1) Worst Case Access Time|first1=Michael L.|last1=Fredman|author1-link=Michael Fredman|first2=János|last2=Komlós|first3=Endre|last3=Szemerédi|author3-link=Endre Szemerédi|journal=[[Journal of the ACM]]|volume=31|issue=3|year=1984|doi=10.1145/828.1884|pages=538}}. A preliminary version appeared in 23rd [[Symposium on Foundations of Computer Science]], 1982, {{doi|10.1109/SFCS.1982.39}}.</ref> [[random matrix|random matrices]],<ref>{{citation|doi=10.1007/BF02579329|first1=Zoltán|last1=Füredi|author1-link=Zoltán Füredi|first2=János|last2=Komlós|title=The eigenvalues of random symmetric matrices|journal=Combinatorica|volume=1|issue=3|year=1981|pages=233–241}}.</ref> the [[Szemerédi regularity lemma]],<ref>{{citation|title=Szemeredi's Regularity Lemma and its applications in graph theory|first1=János|last1=Komlós|first2=Miklós|last2=Simonovits|publisher=Technical Report: 96-10, [[DIMACS]]|year=1996|url=http://dimacs.rutgers.edu/TechnicalReports/abstracts/1996/96-10.html}}.</ref> and [[derandomization]].<ref>{{citation|first1=Miklós|last1=Ajtai|author1-link=Miklós Ajtai|first2=János|last2=Komlós|first3=Endre|last3=Szemerédi|author3-link=Endre Szemerédi|contribution=Deterministic simulation in LOGSPACE|doi=10.1145/28395.28410|title=[[Symposium on Theory of Computing|Proc. 19th ACM Symposium on Theory of Computing]]|year=1987|pages=132–140}}.</ref>
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| ==Degrees, awards==
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| Komlós received his Ph.D. in 1967 from [[Eötvös Loránd University]] under the supervision of [[Alfréd Rényi]].<ref>{{mathgenealogy|id=47880|name=János Komlós}}.</ref> 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]].<ref>[http://www.math.rutgers.edu/people/faculty-honors.html Rutgers Mathematics Department – Recent Faculty Honors].</ref>
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| ==See also==
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| * [[Komlós–Major–Tusnády approximation]]
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| ==References==
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| {{reflist}}
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| {{Authority control|VIAF=165950875}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Komlos, Janos
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Hungarian mathematician
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| | DATE OF BIRTH = 23 May 1942
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| | PLACE OF BIRTH =
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Komlos, Janos}}
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| [[Category:1942 births]]
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| [[Category:Living people]]
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| [[Category:Hungarian mathematicians]]
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| [[Category:Members of the Hungarian Academy of Sciences]]
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| [[Category:Theoretical computer scientists]]
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I'm Vickey (31) from Laugarvatn, Iceland.
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