Abstract
In this session, we complete the proof of strong spectral convergence for the model of regular random graph configurations, using Joel Friedman's method. In parallel, we begin to introduce the polynomial method (Chen--Garza-Vargas--Tropp--Van Handel 2024) and compare the two methods.
References:
- 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.
- C-F. Chen, J. Garza-Vargas, J. A. Tropp, R. van Handel, A new approach to strong convergence, arXiv:2405.1602
