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pro vyhledávání: '"Wood, Philip A"'
Autor:
O'Rourke, Sean, Wood, Philip Matchett
We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz matrix, where the bandwidth is allowed to grow slowly with the dimensio
Externí odkaz:
http://arxiv.org/abs/2106.04785
Autor:
O'Rourke, Sean, Wood, Philip Matchett
Publikováno v:
In Linear Algebra and Its Applications 15 January 2023 657:50-126
For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions on the entries of each matrix, it is known that the limiting empirical
Externí odkaz:
http://arxiv.org/abs/1711.07420
Autor:
Wang, Ke, Wood, Philip Matchett
In this note, we give a precise description of the limiting empirical spectral distribution (ESD) for the non-backtracking matrices for an Erd\H{o}s-R\'{e}nyi graph assuming $np/\log n$ tends to infinity. We show that derandomizing part of the non-ba
Externí odkaz:
http://arxiv.org/abs/1710.11015
Autor:
Borst, Christian, Boyd, Evan, Brekken, Claire, Solberg, Samantha, Wood, Melanie Matchett, Wood, Philip Matchett
We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic polynomia
Externí odkaz:
http://arxiv.org/abs/1705.03709
Publikováno v:
Duke Math. J. 168, no. 3 (2019), 377-427
In this paper we give a conjecture for the average number of unramified $G$-extensions of a quadratic field for any finite group $G$. The Cohen-Lenstra heuristics are the specialization of our conjecture to the case that $G$ is abelian of odd order.
Externí odkaz:
http://arxiv.org/abs/1702.04644
Autor:
O'Rourke, Sean, Wood, Philip Matchett
Motivated by the question of whether a random polynomial with integer coefficients is likely to be irreducible, we study the probability that a monic polynomial with integer coefficients has a low-degree factor over the integers, which is equivalent
Externí odkaz:
http://arxiv.org/abs/1608.01938
Autor:
O'Rourke, Sean, Wood, Philip Matchett
We consider the eigenvalues and eigenvectors of matrices of the form M + P, where M is an n by n Wigner random matrix and P is an arbitrary n by n deterministic matrix with low rank. In general, we show that none of the eigenvalues of M + P need be r
Externí odkaz:
http://arxiv.org/abs/1510.00039
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