Model of random graphs. For more information about these models, see [6, 35]. We denote this graph by Gn,d. It is important to notice that the edges of Gn,d are not independent. Because of this, this model is usually harder to study, compared to G n, p. In the whole paper, we assume that n is large.
All logarithms have natural base, if not specified otherwise. Let pn be the probability that Mn is singular.
Conjecture 2. Theorem 2. Their arguments were simplified by Tao and Vu in [66], resulting in a slightly better bound O. Shortly afterwards, these authors [67] combined the approach from [37] with the idea of inverse theorems see [71, Chapter 7] or [53] for surveys to obtained a more significant improvement Theorem 2. With an additional twist, Bourgain, Vu and Wood [9] improved the bound further Theorem 2. The method from [67, 9] enables one to deduce bounds on pn directly from simple trigonometrical estimates.
The problem of estimating pv came from a paper of Littlewood and Offord in the s [45], as a key technical ingredient in their study of real roots of random polynomials. Small ball inequality Let v1 ,. To give the reader a feeling about how small ball estimates can be useful in estimating pn , let us expose the rows of Mn one by one from top to bottom.
In Section 3, the reader will see an application of Theorem 2.
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In order to obtain the stronger estimates in Theorems 2. These theorems are motivated by inverse theorems of Freiman type in Additive Combinatorics, the discussion of which is beyond the scope of this survey. The interested reader is referred to [53] for a detailed discussion. Fact 3. Then H contains at most 2d Bernoulli vectors.
To see this, notice that in a subspace of dimension d, there is a set of d coordinates which determine the others. The following lemma implies the theorem via the union bound. Lemma 3. If we fix such v and let X be a random Bernoulli vector, then by Theorem 2. Alon, Eigenvalues and expanders, Combinatorica 6 , no.
Alon and V. Theory Ser. B 38 , no.
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Alon and J. Spencer, The probabilistic method, 3rd ed. Arratia and S. Bai and J. Silverstein, Spectral analysis of large dimensional random matrices. Second edition. Springer Series in Statistics. Springer, New York, Second edition, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, Set systems, hypergraphs, families of vectors and combinatorial probability.
Bordenave, M. Lelarge, and J. Salez, The rank of diluted random graphs, Ann. Bourgain, V. Vu and P. Wood, On the singularity probability of discrete random matrices, J. Brooks and E. Lindenstrauss, Non-localization of eigenfunctions on large regular graphs, Israel J. Quasirandom graphs. Combinatorica 9 , no. Costello and V. Vu, The ranks of random graphs. Random Structures and Algorithm.
Vu, The rank of sparse random matrices, Combin. Costello, T. Tao and V. Vu, Random symmetric matrices are almost surely singular, Duke Math. Dekel, J. Lee, and N. Eigenvectors of random graphs: Nodal domains. Approx- imation, Randomization, and Combinatorial Optimization.
Algorithms and Techniques, pages , Dimitriu and S. Pal, Sparse regular random graphs: spectral density and eigenvectors, Ann. Edelman, E.
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Kostlan and M. Shub, How many eigenvalues of a random matrix are real? Matrix Anal. Knowles, H-T.
Yau and J. Yin, Spectral statistics of Erd? Schlein and H-T. Yau, Wegner estimate and level repulsion for Wigner random matrices, Int. IMRN , no. Yau, Universality of local spectral statistics of random matrices, Bull. On the second eigenvalue and random walks in random d-regular graphs. English summary Mem. Friedman and D-E. Furedi and J.
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Komlós, The eigenvalues of random symmetric matrices,Combinatorica 1 , no. Girko, A refinement of the central limit theorem for random determinants. Russian Teor. Girko, A central limit theorem for random determinants. Guionnet and O. Zeitouni, Concentration of the spectral measure for large matrices, Electron.
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