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Normality and Gaussian Perturbation.
~
Deneanu, Andrei Florin.
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Normality and Gaussian Perturbation.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Normality and Gaussian Perturbation./
作者:
Deneanu, Andrei Florin.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:
72 p.
附註:
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Contained By:
Dissertations Abstracts International81-04B.
標題:
Applied mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13808897
ISBN:
9781687910509
Normality and Gaussian Perturbation.
Deneanu, Andrei Florin.
Normality and Gaussian Perturbation.
- Ann Arbor : ProQuest Dissertations & Theses, 2019 - 72 p.
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Thesis (Ph.D.)--Yale University, 2019.
This item must not be sold to any third party vendors.
In this thesis, we address two selected topics in random matrices. In Chapter 1 we consider the problem of bounding the probability that a random matrix with Bernoulli entries taking values ±1 with equal probabilities is normal. We prove that the probability is between 2-n2/2+o(n2) and 2-0.3⋅n2+o(n2) and we conjecture that the probability is in fact 2-n2/2+o(n2), which is asymptotically the same with the probability that it is symmetric.Chapter 2 addresses an interesting problem concerning the perturbation of matrices. We investigate how the spectral norm of a deterministic Hermitian matrix changes under the addition of Gaussian noise. We consider An ∈ ℂnxn to be a deterministic Hermitian matrix for some large integer n with ordered eigenvalues λ1 > λ2 ≥ ... ≥ λn. We prove that if λ1 - λk > Ck log k(log log k)1+δ for some constant C > 0 and small constant δ > 0, the spectral norm of the perturbed operator is the same as that of An, except for the addition of a Gaussian random variable with mean 0 and with variance 1 when perturbed by GUE matrix, and with variance $2$ when perturbed by a GOE matrix. We prove that the powers of k and log k in the condition are optimal.
ISBN: 9781687910509Subjects--Topical Terms:
2122814
Applied mathematics.
Subjects--Index Terms:
Perturbation
Normality and Gaussian Perturbation.
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