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Hungarian-American mathematician
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 ct 2 /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
1
2
n
log
n
+
1
2
n
log
log
n
+
c
n
{\displaystyle {\frac {1}{2}}n\log n+{\frac {1}{2}}n\log \log n+cn}
edges, where c is a fixed real number, then the probability that G has a
Hamiltonian circuit converges to
e
−
e
−
2
c
.
{\displaystyle e^{-e^{-2c}}.}
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.
^
Ajtai, Miklós ; Komlós, János;
Szemerédi, Endre (1983), "An O(n log n ) sorting network",
Proc. 15th ACM Symposium on Theory of Computing , pp. 1–9,
doi :
10.1145/800061.808726 ,
S2CID
15311122 ;
Ajtai, Miklós ; Komlós, János;
Szemerédi, Endre (1983), "Sorting in c log n parallel steps", Combinatorica , 3 (1): 1–19,
doi :
10.1007/BF02579338 ,
S2CID
519246 .
^ J. Komlós, G. Sárközy, Szemerédi: Blow-Up Lemma,
Combinatorica , 17 (1997), 109–123.
^ Komlós, J.;
Pintz, J. ;
Szemerédi, E. (1982), "A lower bound for Heilbronn's problem",
Journal of the London Mathematical Society , 25 (1): 13–24,
doi :
10.1112/jlms/s2-25.1.13
^ Komlós, J.; Major, P.; Tusnády, G. (1975), "An approximation of partial sums of independent RV'-s, and the sample DF. I", Probability Theory and Related Fields , 32 (1–2): 111–131,
doi :
10.1007/BF00533093 ,
S2CID
8272486 .
^
Fredman, Michael L. ; Komlós, János;
Szemerédi, Endre (1984), "Storing a Sparse Table with O(1) Worst Case Access Time",
Journal of the ACM , 31 (3): 538,
doi :
10.1145/828.1884 ,
S2CID
5399743 . A preliminary version appeared in 23rd
Symposium on Foundations of Computer Science , 1982,
doi :
10.1109/SFCS.1982.39 .
^
Füredi, Zoltán ; Komlós, János (1981), "The eigenvalues of random symmetric matrices", Combinatorica , 1 (3): 233–241,
doi :
10.1007/BF02579329 ,
S2CID
7847476 .
^ Komlós, János; Simonovits, Miklós (1996),
Szemeredi's Regularity Lemma and its applications in graph theory , Technical Report: 96-10,
DIMACS .
^
Ajtai, Miklós ; Komlós, János;
Szemerédi, Endre (1987), "Deterministic simulation in LOGSPACE",
Proc. 19th ACM Symposium on Theory of Computing , pp. 132–140,
doi :
10.1145/28395.28410 ,
S2CID
15323404 .
^
János Komlós at the
Mathematics Genealogy Project .
^
Rutgers Mathematics Department – Recent Faculty Honors
Archived 2008-12-18 at the
Wayback Machine .