Đề tài " Invertibility of random matrices: norm of the inverse " doc

... ·   A −1   plays the crucial role. Since the norm of A is usually highly concentrated, the distortion is determined by the norm of A −1 . The estimate of the norm of A −1 is known only in the case *Research ... and the size of the ε-net using Lemma 8.1. Note that only the second estimate uses the profile of the vectors. Then we conclude the proof...

Ngày tải lên: 15/03/2014, 09:20

... positivity. In other words, u 0 is a completely positive mapping. This concludes the proof. In Section 7, we shall need the following strengthening of Theorem 2.2: 2.4 Theorem. Assume that the self ... ,r. Before the proof of Theorem 2.2, we make a few observations: 2.3 Remark. (1) In connection with condition (2.1) above, let V be a subspace of M m (C) containing the unit 1 1...

Ngày tải lên: 22/03/2014, 20:20

... results of [Koz] and of the proof of the renormalization theorem in [LvS] provides Theorem 2.3. The outline of the proof is given in Appendix 5.3. Theorem 2.1 is a trivial consequence of Theorems ... connected component of the domain B. Then the ratio |A k l +1 | |A k l | tends to 0 exponentially fast, where |A k | is the length of the real trace of the domai...

Ngày tải lên: 05/03/2014, 23:20

... have the action of G m on Gr X n via the cocharacter 2ˇρ. The fixed point set of this action consists of the locus of products of the fixed points in the individual affine Grassmannians, i.e., above the ... through the rest of the paper in the case when k is a field of characteristic zero. The arguments of Section 12, in a greatly simplified form, then give The...

Ngày tải lên: 06/03/2014, 08:21

... CURVES 383 2.3. Proof of Theorem 5. To a certain degree the proof follows the same line of argument as the proof of the convergent part of Theorem 2. In par- ticular, it suffices to consider the rational ... <ψ(Q)/Q  . Proof of Theorem 6 modulo Theorem 7. This is trivial. Given the hy- potheses of Theorem 7, the hypotheses of Theorem 6 are clearly satisfied. Fix a...

Ngày tải lên: 15/03/2014, 09:20

... (4) that is, the mean of w n+1 − w n is 1. The zeta function is central to the theory of the distribution of the prime numbers. This fact follows directly from the representation of the zeta function as ... methods of theoretical physics. One important unifying ground, and also a mathematical basis for the Random Matrix Theory, is the concept of integrability....

Ngày tải lên: 22/03/2014, 09:20

... with the order of magnitude, for the rest of the proof for Theorem 3.1 in Sections 4–6, we shall replace ω(p) by p 2 whenever it is more convenient. 4.3. The upper bound of the diagonal term: The ... ω(p n−1 )  .(4.29) Under the assumptions (3.9) (3.10), the term on the right side of (4.28) is much smaller than the accuracy we need for Theorem 3.1. Therefore this...

Ngày tải lên: 22/03/2014, 16:20

... exp(Cn 1+δ ).(3.4) The strategy for the proof of this theorem is the same as the strategy of the proof of Theorem 1.3.9 described in Chapter 2. Denote the supremum C 2 and C 1 -norms of the family (3.1) M 1 = ... C 2 -smooth maps of the interval I =[−1, 1] In Section 2.4 we concluded that the key to the proof of Theorem 1.3.9 (which implies the Main Theorem)...

Ngày tải lên: 29/03/2014, 07:20

... understood the term, in his mind there Clerambault 101 could be no other. After this there was no need for the vociferations of the papers; in the author of " ;The Appeal to the Living," and the ... Gillot. They had read the evening papers which gave an account of the incident from their point of view; some spoke of the "spontaneous" indignation...

Ngày tải lên: 18/02/2014, 08:20

... operations. The ranks of the column spaces of a matrix do not change after row operations. Hence, the rank of B  equals the rank of B. Moreover, the rank of the column space → P (r −1,s− 1, 1) of B  remains ... well-defined over M g,n : the fiber over a nodal curve C is defined to be the space of sections of the dualizing sheaf of C. Let λ g be the top Che...

Ngày tải lên: 05/03/2014, 23:20