Strong Uniform Expansion in SL(2, p)

Geometric and Functional Analysis

Volumn 20, Issue 5, 2010, Pages 1201-1209

  Breuillard, Emmanuel ^a   Gamburd, Alex ^b  

^a UNIVERSITÉ PARIS SUD   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Expander graphs; finite groups; random walks; Tits alternative

Indexed keywords

EID: 78549296443     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-010-0094-3     Document Type: Article

References (26)

1. Abert M., Babai L.: Finite groups of uniform logarithmic diameter. Israel J. Math. 158, 193-203 (2007).
2. N. Alon, A. Lubotzky, A. Wigderson, Semi-direct product in groups and zig-zag product in graphs: Connections and applications, Proc. of the 42nd FOCS (2001), 630-637.
3. E. Breuillard, A strong Tits alternative, preprint (2008); arXiv: 0804. 1395.
4. E. Breuillard, Heights on SL(2) and free subgroups, Zimmer's Festschrift, Chicago Univ. Press, to appear.
5. p). Annals of Mathematics 167, 625-642 (2008).
6. Celler F., Leedham-Green C. R., Murray S., Niemeyer A., O'Brien E. A.: Generating random elements of a finite group. Comm. Algebra 23, 4931-4948 (1995).
7. Gamburd A., Pak I.: Expansion of product replacement graphs. Combinatorica 26, 411-429 (2006).
8. Gilman R.: Finite quotients of the automorphism group of a free group. Canad. J. Math. 29, 541-551 (1977).
9. G. Hoheisel, Primzahlprobleme in der analysis, S-B Preuss. Akad. Wiss. Phys.- Math. Kl (1930), 580-588.
10. Hoory S., Linial N., Wigderson A.: Expander graphs and their applications. Bull. Amer. Math Soc. 43, 439-561 (2006).
11. Huxley M. N.: On the difference between consecutive primes. Invent. Math. 15, 164-170 (1972).
12. Kassabov M.: Symmetric groups and expander graphs. Invent. Math. 170, 327-354 (2007).
13. Kesten H.: Symmetric random walks on groups. Trans. AMS 92, 336-354 (1959).
14. E. Kowalski, H. Iwaniec, Analytic Number Theory, AMS Colloquium Publication 53 (YEAR).
15. A. Lubotzky, Discrete Groups, Expanding Graphs and Invariant Measures, Progress in Mathematics 195, Birkhäuser (1994).
16. A. Lubotzky, Cayley graphs: eigenvalues, expanders and random walks, Surveys in Combinatorics (P. Rowbinson, ed.), London Math. Soc. Lecture Note Ser. 218, Cambridge Univ. Press (1995), 155-189.
17. Lubotzky A., Pak I.: The product replacement algorithm and Kazhdan's property (T). Journal of AMS 52, 5525-5561 (2000).
18. Lubotzky A., Phillips R., Sarnak P.: Ramanujan graphs. Combinatorica 8, 261-277 (1988).
19. A. Lubotzky, B. Weiss, Groups and Expanders, in "DIMACS Series in Disc. Math. and Theor. Comp. Sci. 10 (J. Friedman, ed.) (1993), 95-109.
20. Margulis G. A.: Explicit constructions of concentrators. Probl. of Inform. Transm. 10, 325-332 (1975).
21. Margulis G. A.: Explicit group-theoretic constructions of combinatorial schemes and their applications in the construction of expanders and concentrators. Probl. of Inform. Trans. 24, 39-46 (1988).
22. D. W. Masser, G. Wustholz, Fields of large transcendence degree generated by values of elliptic functions, Invent. Math. (1983), 407-464.
23. I. Pak, What do we know about the product replacement algorithm?, in "Groups and Computation III" (W. Kantor, A. Seress, eds.), Berlin (2000), 301-347.
24. Reingold O., Vadhan S., Wigderson A.: Entropy waves, the zig-zag graph product, and new constant-degree expanders. Annals of Mathematics 155(1), 157-187 (2002).
25. Sarnak P.: What is an expander?. Notices of the American Mathematical Society 51, 762-763 (2004).
26. Suzuki M.: Group Theory I. Springer-Verlag, Berlin-Heidelberg-New York (1982).