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词条 János Komlós (mathematician)
释义

  1. Notable results

  2. Degrees, awards

  3. See also

  4. References

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[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

  • 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

  • Komlós–Major–Tusnády approximation

References

1. ^Rutgers faculty profile for Komlós.
2. ^UCSD Maths Dept history {{webarchive|url=https://web.archive.org/web/20081028083525/http://math.ucsd.edu/about/history/ |date=2008-10-28 }}
3. ^M. Ajtai, J. Komlós, E. Szemerédi: A note on Ramsey numbers, J. Combin. Theory Ser. A, 29(1980), 354–360.
4. ^{{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=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}}.
5. ^J. Komlós, G. Sárközy, Szemerédi: Blow-Up Lemma, Combinatorica, 17(1997), 109–123.
6. ^{{citation|last1=Komlós|first1=J.|author2-link=János Pintz|last2=Pintz|first2=J.|last3=Szemerédi|first3=E.|author3-link=Endre Szemerédi|title=A lower bound for Heilbronn's problem|journal=Journal of the London Mathematical Society|volume=25|issue=1|pages=13–24|year=1982|doi=10.1112/jlms/s2-25.1.13}}
7. ^{{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}}.
8. ^{{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}}.
9. ^{{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}}.
10. ^{{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}}.
11. ^{{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=Proc. 19th ACM Symposium on Theory of Computing|year=1987|pages=132–140}}.
12. ^{{mathgenealogy|id=47880|name=János Komlós}}.
13. ^Rutgers Mathematics Department – Recent Faculty Honors {{Webarchive|url=https://web.archive.org/web/20081218050113/http://math.rutgers.edu/people/faculty-honors.html# |date=2008-12-18 }}.
{{Authority control}}{{DEFAULTSORT:Komlos, Janos}}

7 : 1942 births|Living people|Hungarian mathematicians|Members of the Hungarian Academy of Sciences|Theoretical computer scientists|Eötvös Loránd University alumni|Rutgers_University_faculty
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