# János Komlós (mathematician)

**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 L
^{1}-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 ξ_{1},ξ_{2},... be a sequence of random variables such that*E*[ξ_{1}],*E*[ξ_{2}],... is bounded. Then there exist a subsequence ξ'_{1}, ξ'_{2},... and a random variable β such that for each further subsequence η_{1},η_{2},... of ξ'_{0}, ξ'_{1},... we have (η_{1}+...+η_{n})/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

- 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

## References

- Rutgers faculty profile for Komlós.
- 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; Ajtai, Miklós; Komlós, János; Szemerédi, Endre (1983), "Sorting in*c*log*n*parallel steps",*Combinatorica*,**3**(1): 1–19, doi:10.1007/BF02579338. - 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. - 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. 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. - 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. - János Komlós at the Mathematics Genealogy Project.
- Rutgers Mathematics Department – Recent Faculty Honors Archived 2008-12-18 at the Wayback Machine.

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