Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model

Wiktor Oktaba

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Displaying similar documents to “Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model”

The unit group of some fields of the form $ℚ (\sqrt{2}, \sqrt{p}, \sqrt{q}, \sqrt{- l})$

Moha Ben Taleb El Hamam (2024)

Mathematica Bohemica

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Let $p$ and $q$ be two different prime integers such that $p \equiv q \equiv 3 (mod 8)$ with $(p / q) = 1$ , and $l$ a positive odd square-free integer relatively prime to $p$ and $q$ . In this paper we investigate the unit groups of number fields $𝕃 = ℚ (\sqrt{2}, \sqrt{p}, \sqrt{q}, \sqrt{- l})$ .

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

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For a real square matrix $A$ and an integer $d \geq 0$ , let $A_{(d)}$ denote the matrix formed from $A$ by rounding off all its coefficients to $d$ decimal places. The main problem handled in this paper is the following: assuming that $A_{(d)}$ has some property, under what additional condition(s) can we be sure that the original matrix $A$ possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists...

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.

On bilinear forms based on the resolvent of large random matrices

Walid Hachem, Philippe Loubaton, Jamal Najim, Pascal Vallet (2013)

Annales de l'I.H.P. Probabilités et statistiques

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Consider a $N \times n$ non-centered matrix $𝛴_{n}$ with a separable variance profile: $𝛴_{n} = \frac{D_{n}^{1 / 2} X_{n} {\tilde{D}}_{n}^{1 / 2}}{\sqrt{n}} + A_{n} .$ Matrices $D_{n}$ and ${\tilde{D}}_{n}$ are non-negative deterministic diagonal, while matrix $A_{n}$ is deterministic, and $X_{n}$ is a random matrix with complex independent and identically distributed random variables, each with mean zero and variance one. Denote by $Q_{n} (z)$ the resolvent associated to $𝛴_{n} 𝛴_{n}^{*}$ , i.e. $Q_{n} (z) = {(𝛴_{n} 𝛴_{n}^{*} - z I_{N})}^{- 1} .$ Given two sequences of deterministic vectors $(u_{n})$ and $(v_{n})$ with bounded Euclidean norms, we study the limiting behavior of the random bilinear form:...

Bicyclotomic polynomials and impossible intersections

David Masser, Umberto Zannier (2013)

Journal de Théorie des Nombres de Bordeaux

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In a recent paper we proved that there are at most finitely many complex numbers $t \neq 0, 1$ such that the points $(2, \sqrt{2 (2 - t)})$ and $(3, \sqrt{6 (3 - t)})$ are both torsion on the Legendre elliptic curve defined by $y^{2} = x (x - 1) (x - t)$ . In a sequel we gave a generalization to any two points with coordinates algebraic over the field $Q (t)$ and even over $C (t)$ . Here we reconsider the special case $(u, \sqrt{u (u - 1) (u - t)})$ and $(v, \sqrt{v (v - 1) (v - t)})$ with complex numbers $u$ and $v$ .

Investigating generalized quaternions with dual-generalized complex numbers

Nurten Gürses, Gülsüm Yeliz Şentürk, Salim Yüce (2023)

Mathematica Bohemica

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We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $α$ , $β$ and $𝔭$ . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.

Displaying similar documents to “Asymptotically normal confidence intervals for a determinant in a generalized multivariate Gauss-Markoff model”

The unit group of some fields of the form ℚ ( 2 , p , q , - l )

Ground states of supersymmetric matrix models

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

On the matrix negative Pell equation

On bilinear forms based on the resolvent of large random matrices

Bicyclotomic polynomials and impossible intersections

Investigating generalized quaternions with dual-generalized complex numbers

The unit group of some fields of the form $ℚ (\sqrt{2}, \sqrt{p}, \sqrt{q}, \sqrt{- l})$