Non-localization of eigenfunctions on large regular graphs

Israel Journal of Mathematics

Volumn 193, Issue 1, 2013, Pages 1-14

  Brooks, Shimon ^a   Lindenstrauss, Elon ^b  

^a STONY BROOK UNIVERSITY   (United States)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84876114544     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/s11856-012-0096-y     Document Type: Article

References (12)

1. N. Anantharaman and S. Nonnenmacher, Half-delocalization of eigenfunctions for the Laplacian on an Anosov manifold, Université de Grenoble. Annales de l'Institut Fourier 57 (2007), 2465-2523.
2. R. Brooks, The spectral geometry of k-regular graphs, Journal d'Analyse Mathématique 57 (1991), 120-151.
3. S. Brooks, Entropy bounds for quantum limits, Ph. D. thesis, Princeton University, 2009.
4. S. Brooks and E. Lindenstrauss, Graph eigenfunctions and quantum unique ergodicity, Comptes Rendus Mathématique. Académie des Sciences. Paris 348 (2010), 829-834.
5. A. Figá-Talamanca and M. Picardello, Harmonic Analysis on Free Groups, Lecture Notes in Pure and Applied Mathematics, Vol. 87, Marcel Dekker Inc., New York, 1983.
6. ∞Norms of eigenfunctions of arithmetic surfaces, Annals of Mathematics 141 (1995), 301-320.
7. E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Annals of Mathematics 163 (2006), 165-219.
8. B. McKay, N. Wormald and B. Wysocka, Short cycles in random regular graphs, Electronic Journal of Combinatorics 11 (2004).
9. Z. Rudnick and P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Communications in Mathematical Physics 161 (1994), 195-213.
10. L. Silberman and A. Venkatesh, On quantum unique ergodicity for locally symmetric spaces, Geometric and Functional Analysis 17 (2007), 960-998.
11. 2(ℤ)\ℍ, Annals of Mathematics 172 (2010), 1529-1538.
12. A. Terras and D. Wallace, Selberg's trace formula on the k-regular tree and applications, International Journal of Mathematics and Mathematical Sciences 8 (2003), 501-526.