Expansion and random walks in SLd(ℤ/pnℤ): I

Journal of the European Mathematical Society

Volumn 10, Issue 4, 2008, Pages 987-1011

  Bourgain, Jean ^a   Gamburd, Alex ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56649109576     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/137     Document Type: Article

References (26)

1. Bougerol, P., Lacroix, J.: Products of Random Matrices with Applications to Schrödinger Operators. Progr. Probab. Statist. 8, Birkhäuser (1985) Zbl 0572.60001 MR 0886674
2. q arbitrary. Preprint (2007)
3. p). Ann. of Math. 167, 625-642 (2008) MR 2415383
4. Bourgain, J., Gamburd, A.: On the spectral gap for finitely-generated subgroups of SU(2). Invent. Math. 171, 83-121 (2008) Zbl 1135.22010 MR 2358056
5. nℤ): II. Preprint
6. Bourgain, J., Gamburd, A., Sarnak, P.: Affine linear sieve, expanders, and sum-product. Preprint
7. Bourgain, J., Glibichuk, A., Konyagin, S.: Estimate for the number of sums and products and for exponential sums in fields of prime order. J. London Math. Soc. 73, 380-398 (2006) Zbl 1093.11057 MR 2225493
8. Bourgain, J., Katz, N., Tao, T.: A sum-product estimate in finite fields and applications. Geom. Funct. Anal. 14, 27-57 (2004) Zbl pre02121750 MR 2053599
9. Cassels, J. W. S.: Rational Quadratic Forms. Academic Press (1978) Zbl 0395.10029 MR 0522835
10. Clifford, A. H.: Representations induced in an invariant subgroup. Ann. of Math. 38, 533-550 (1937) Zbl 0017.29705 MR 1503352
11. Dawson, C. M., Nielsen, M. A.: The Solovay-Kitaev algorithm. Quantum Information Cornput. 6, 81-95 (2006) MR 2212257
12. 2(ℤ). Israel J. Math. 127, 157-200(2002) Zbl 1028.11031 MR 1900698
13. Gamburd, A., Shahshahani, M.: Uniform diameter bounds for some families of Cayley graphs. Int. Math. Res. Notices 2004, no. 71, 3813-3824 Zbl 1066.05072 MR 2104475
14. 2(ℤ/pℤ). Ann. of Math. 167, 601-623 (2008) MR 2415382
15. Hoory, S., Linial, N., Wigderson, A.: Expander graphs and their applications. Bull. Amer. Math. Soc. 43, 439-561 (2006) MR 2247919
16. Kesten, H.: Symmetric random walks on groups. Trans. Amer. Math. Soc. 92, 336-354 (1959) Zbl 0092.33503 MR 0109367
17. Lubotzky, A.: Discrete Groups, Expanding Graphs and Invariant Measures. Progr. Math. 125, Birkhäuser (1994) Zbl 0826.22012 MR 1308046
18. Lubotzky, A.: Cayley graphs: eigenvalues, expanders and random walks. In: Surveys in Combinatorics, P. Rowlinson (ed.), London Math. Soc. Lecture Note Ser. 218, Cambridge Univ. Press, 155-189(1995) Zbl 0835.05033 MR 1358635
19. Lubotzky, A., Weiss, B.: Groups and expanders. In: Expanding Graphs (Princeton, NJ, 1992), DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 10, J. Friedman (ed.), Amer. Math. Soc., 95-109(1993) Zbl 0787.05049 MR 1235570
20. Sarnak, P.: What is an expander? Notices Amer. Math. Soc. 51, 762-763 (2004) Zbl pre02115090 MR 2072849
21. Sarnak, P., Xue, X.: Bounds for multiplicities of automorphic representations. Duke Math. J. 64, 207-227(1991) Zbl 0741.22010 MR 1131400
22. Selberg, A.: On the estimation of Fourier coefficients of modular forms. In: Proc. Sympos. Pure Math. 8, Amer. Math. Soc, 1-15(1965) Zbl 0142.33903 MR 0182610
23. Shalom, Y.: Expanding graphs and invariant means. Combinatorica 17, 555-575 (1997) Zbl 0906.05027 MR 1645694
24. Shalom, Y.: The algebraization of Kazhdan's property (T). In: Int. Congress of Math. Vol. II, Eur. Math. Soc, 1283-1310 (2006) Zbl 1109.22003 MR 2275645
25. Tao, T.: Product sets estimates for non-commutative groups. Preprint (2005)
26. Tao, T., Vu, V.: Additive Combinatorics. Cambridge Univ. Press (2006) Zbl 1127.11002 MR 2289012