Corrections to published papers
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- with N. Alon, I. Benjamini, E. Lubetzky, Non-backtracking random walks mix faster, arXiv:math/0610550: we should have mentioned that Theorem 1.1 is closely
related to the cogrowth formula for discrete groups which was found in the works:
R. I. Grigorchuk,
Symmetric random walks on discrete groups,
Uspehi Mat. Nauk 32 (1977), no. 6 (198), 217–218
J. M. Cohen,
Cogrowth and amenability of discrete groups.
J. Funct. Anal. 48 (1982), no. 3, 301–309.
and even more so to its version for regular graphs, proved in
Cogrowth of regular graphs.
Proc. Amer. Math. Soc. 116 (1992), no. 1, 203–205.
- with O. N. Feldheim, A universality result for the smallest eigenvalues of certain sample covariance matrices, arXiv:0812.1961: on p.7 of the arxiv version, par. 4, we should have mentioned the work:
T. H. Baker, P. J. Forrester, and P. A. Pearce. Random matrix ensembles with an effective extensive external charge. J. Phys. A. Math. Gen., 31(29):6087–6101, July 1998
who found the scaling limit at the left edge of the (Gaussian) Laguerre ensemble with aspect ratio bounded from 1 (in our
notation, B(N)inv with M(N)/N → c < 1)
- The Tracy–Widom law for some sparse random matrices, arXiv:0903.4295. the proof contains a serious mistake, and Lemma 5 can not be true as stated. For example, the probability that the graph is not connected tends to zero slower than eq. 4 would imply. I am grateful to Charles Bordenave and Sandrine Péché who brought this to my attention.
- The spectral edge of some random band matrices, arXiv:0906.4047, Section 3: there are several mistakes in the proofs of the Central Limit Theorem on the circle (Lemmata 3.1 – 3.3), the most serious of which is that the estimate in Lemma 3.5 (stated without proof) is wrong. Still, Lemmata 3.1 – 3.3 are valid as stated (corrected proofs are available upon request), and thus the validity of the other
parts of the paper, particularly, of the main results, is not impaired.
- A limit theorem at the spectral edge for corners of time-dependent Wigner matrices, arXiv:1312.1007: several formulae in Section 3 require corrections which do not impair the validity of the results. These corrections are listed in Remark 2.17 of the paper arXiv:1604.01104.