Abstract
Having finished stating the consequences of convergence in the sense of Benjamini and Schramm for sequences of measured metric spaces, we turn to the notion of strong spectral convergence. The next sessions will be devoted to the case of random regular graph models and Joel Friedman's demonstration of almost certain strong spectral convergence.
References
- M. Abert, N. Bergeron, I. Biringer, T. Gelander, N. Nikolov, J. Raimbault, I. Samet. On the growth of L^2-invariants for sequences of lattices in Lie groups. Annals of Mathematics 185 (2017), 711-790.
- L. Bowen. Cheeger constants and L^2 Betti numbers. Duke Math. J. 164 (3): 569-615.
- J. Friedman. On the second eigenvalue and random walks in random d-regular graphs. Combinatorica, Volume 11, pages 331-362, (1991).
- J. Friedman. A proof of Alon's second eigenvalue conjecture and related problems. Mem. Amer. Math. Soc. 195(910), 2008.
- J. Friedman, D. Kohler. On the relativized Alon eigenvalue conjecture II: Asymptotic expansion theorems for walks. arXiv:1911.05705, 2019.
