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pro vyhledávání: '"Bouthat, Ludovick"'
A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem suggests a broad generalization: the construction of so-called random v
Externí odkaz:
http://arxiv.org/abs/2403.10314
Autor:
Bouthat, Ludovick
In a recent article, Ch\'avez, Garcia and Hurley introduced a new family of norms $\|\cdot\|_{\mathbf{X},d}$ on the space of $n \times n$ complex matrices which are induced by random vectors $\mathbf{X}$ having finite $d$-moments. Therein, the author
Externí odkaz:
http://arxiv.org/abs/2402.08173
Autor:
Bouthat, Ludovick, Chávez, Ángel, Fullerton, Sarah, LaFortune, Matilda, Linarez, Keyron, Liyanage, Nethmin, Son, Justin, Ting, Tyler
Recent work shows that a new family of norms on Hermitian matrices arise by evaluating the even degree complete homogeneous symmetric (CHS) polynomials on the eigenvalues of a Hermitian matrix. The CHS norm of a graph is then defined by evaluating th
Externí odkaz:
http://arxiv.org/abs/2311.04689
Autor:
Bouthat, Ludovick
Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still of great importance, particularly in approximation theory and interpol
Externí odkaz:
http://arxiv.org/abs/2311.01208
In the first of this series of two articles, we studied some geometrical aspects of the Birkhoff polytope, the compact convex set of all $n \times n$ doubly stochastic matrices, namely the Chebyshev center, and the Chebyshev radius of the Birkhoff po
Externí odkaz:
http://arxiv.org/abs/2310.14043
The geometry of the Birkhoff polytope, i.e., the compact convex set of all $n \times n$ doubly stochastic matrices, has been an active subject of research. While its faces, edges and facets as well as its volume have been intensely studied, other geo
Externí odkaz:
http://arxiv.org/abs/2310.14041
The objective of the present paper is to establish three Hardy-type inequalities in which the arithmetic mean over a sequence of non-negative real numbers is replaced by some weighted arithmetic mean over some nested subsets of the given sequence of
Externí odkaz:
http://arxiv.org/abs/2306.05586
In a celebrated paper of Marcus and Ree (1959), it was shown that if $A=[a_{ij}]$ is an $n \times n$ doubly stochastic matrix, then there is a permutation $\sigma \in S_n$ such that $\sum_{i,j=1}^{n} a_{i,j}^{2} \leq \sum_{i=1}^{n} a_{i,\sigma(i)}$.
Externí odkaz:
http://arxiv.org/abs/2306.05518
Autor:
Bouthat, Ludovick
Le célèbre théorème de Birkhoff affirme que l'espace Dₙ des matrices doublement stochastiques d'ordre n est un polytope convexe dont les matrices de permutation constituent les points extrémaux. De cette structure particulière émerge une str
Externí odkaz:
https://hdl.handle.net/20.500.11794/102464
Publikováno v:
Special Matrices, Vol 12, Iss 1, Pp 635-655 (2024)
The geometry of the compact convex set of all n×nn\times n doubly stochastic matrices, a structure frequently referred to as the Birkhoff polytope, has been an active subject of research as of late. Geometric characteristics such as the Chebyshev ce
Externí odkaz:
https://doaj.org/article/52d90300187d4022b0baaa52ce2abb81
