Non-interactive correlation distillation, inhomogeneous markov chains, and the reverse bonami-beckner inequality

Israel Journal of Mathematics

Volumn 154, Issue , 2006, Pages 299-336

  Mossel, Elchanan ^a   O'Donnell, Ryan ^b   Regev, Oded ^c   Steif, Jeffrey E ^d   Sudakov, Benny ^e  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

^d CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^e PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748524852     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02773611     Document Type: Article

References (39)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.
2. M. Ajtai, J. Komlós and E. Szemerédi, Deterministic simulation in LOGSPACE, in Proceedings of the 19th Annual ACM Symposium on Theory of Computing, ACM, New York, 1987, pp. 132-140.
3. N. Alon, U. Feige, A. Wigderson and D. Zuckerman, Derandomized graph products, Computational Complexity, Birkhäuser, Basel, 1995.
4. N. Alon, G. Kalai, M. Ricklin and L. Stockmeyer, Lower bounds on the competitive ratio for mobile user tracking and distributed job scheduling, Theoretical Computer Science 130 (1994), 175-201.
5. N. Alon, U. Maurer and A. Wigderson, Unpublished results, 1991.
6. N. Alon and J. Spencer, The Probabilistic Method, 2nd edn., Wiley, New York, 2000.
7. K. Amano and A. Maruoka, On learning monotone Boolean functions under the uniform distribution, Lecture Notes in Computer Science 2533, Springer, New York, 2002, pp. 57-68.
8. W. Beckner, Ineqalities in Fourier analysis, Annals of Mathematics 102 (1975), 159-182.
9. M. Ben-Or and N. Linial, Collective coin Sipping, in Randomness and Computation (S. Micali, ed.), Academic Press, New York, 1990.
10. I. Benjamini, G. Kalai and O Schramm, Noise sensitivity of boolean functions and applications to percolation, Publications Mathématiques de l'Institut des Hautes Études Scientifiques 90 (1999), 5-43.
11. S. Bobkov and F. Götze, Discrete isoperimetric and Poincaré-type inequalities, Probability Theory and Related Fields 114 (1999), 245-277.
12. p(G), Annales de l'Institut Fourier 20 (1970), 335-402.
13. C. Borell, Positivity improving operators and hypercontractivity, Mathematische Zeitschrift 180 (1982), 225-234.
14. J. Bourgain, An appendix to Sharp thresholds of graph properties, and the k-sat problem, by E. Friedgut, Journal of the American Mathematical Society 12 (1999), 1017-1054.
15. J. Bourgain, J. Kahn, G. Kalai, Y. Katznelson and N. Linial, The influence of variables in product spaces, Israel Journal of Mathematics 77 (1992), 55-64.
16. J. Bourgain and G. Kalai, Influences of variables and threshold intervals under group symmetries, Geometric and Functional Analysis 7 (1997), 438-461.
17. N. Bshouty, J. Jackson and C. Tamon, Uniform-distribution attribute noise learnability, in Proceedings of the Eighth Annual Conference on Computational Learning Theory, (COLT 1995), Santa Cruz, California, USA, ACM, 1995.
18. I. Dinur, V. Guruswami and S. Khot, Vertex cover on k-uniform hypergraphs is hard to approximate within factor (k-3-ε), ECCC Technical Report TR02-027, 2002.
19. I. Dinur and S. Safra, The importance of being biased, in Proceedings of the 34th Annual ACM Symposium on the Theory of Computing, ACM, New York, 2002, pp. 33-42.
20. W. Feller, An Introduction to Probability Theory and its Applications, 3rd edn., Wiley, New York, 1968.
21. C. Fortuin, P. Kasteleyn and J. Ginibre, Correlation inequalities on some partially ordered sets, Communications in Mathematical Physics 22 (1971), 89-103.
22. E. Friedgut, Boolean functions with low average sensitivity depend on few coordinates, Combinatorica 18 (1998), 474-483.
23. E. Friedgut and G. Kalai, Every monotone graph property has a sharp threshold, Proceedings of the American Mathematical Society 124 (1996), 2993-3002.
24. H. O. Georgii, Gibbs Measures and Phase Transitions, Volume 9 of de Gruyter Studies in Mathematics, de Gruyter, Berlin, 1988.
25. G. Hardy, J. Littlewood and G. Póyla, Inequalities, 2nd edn., Cambridge University Press, 1952.
26. J. Håstad, Some optimal inapproximability results, Journal of the ACM 48 (2001), 798-869.
27. J. Kahn, G. Kalai and N. Linial, The influence of variables on boolean functions, in Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1988, pp. 68-80.
28. S. Khot, On the power of unique 2-prover 1-round games, in Proceedings of the 34th Annual ACM Symposium on the Theory of Computing, ACM, New York, 2002, pp. 767-775.
29. D. Kleitman, Families of non-disjoint subsets, Journal of Combinatorial Theory 1 (1966), 153-155.
30. A. Klivans, R. O'Donnell and R. Servedio, Learning intersections and thresholds of halfspaces, in Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 2002, pp. 177-186.
31. E. Mossel and R. O'Donnell, Coin flipping from a cosmic source: On error correction of truly random bits, Random Structures & Algorithms 26 (2005), 418-436.
32. A. Naor, E. Friedgut and G. Kalai, Boolean functions whose Fourier transform is concentrated on the first two levels, Advances in Applied Mathematics 29 (2002), 427-437.
33. R. O'Donnell, Hardness amplification within NP, in Proceedings of the 34th Annual ACM Symposium on the Theory of Computing, ACM, New York, 2002, pp. 715-760.
34. R. O'Donnell, Computational applications of noise sensitivity, PhD thesis, Massachusetts Institute of Technology, 2003.
35. R. O'Donnell and R. Servedio, Learning monotone decision trees, Manuscript, 2004.
36. R. Raz, Fourier analysis for probabilistic communication complexity, Computational Complexity 5 (1995), 205-221.
37. V. Sazonov, Normal Approximation - Some Recent Advances, Springer-Verlag, Berlin, 1981.
38. M. Talagrand, On Russo's approximate 0-1 law, Annals of Probability 22 (1994), 1476-1387.
39. K. Yang, On the (im)possibility of non-interactive correlation distillation, in LATIN 2004: Theoretical Informatics, 6th Latin American Symposium, Buenos Aires, Argentina, April 5-8, 2004, Proceedings (M. Farach-Colton, ed.), Lecture Notes in Computer Science 2976, Springer, Berlin, 2004.