Relevant bibliographies by topics / Log-concavité

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Academic literature on the topic 'Log-concavité'

Author: Grafiati
Published: 18 May 2024

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Journal articles on the topic "Log-concavité"

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Habsieger, Laurent. "Inégalités entre fonctions symétriques élémentaires: applications à des problèmes de log-concavité." Discrete Mathematics 115, no. 1-3 (1993): 167–74. http://dx.doi.org/10.1016/0012-365x(93)90486-d.

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2

McNamara, Peter R. W., and Bruce E. Sagan. "Infinite log-concavity: developments and conjectures." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AK,..., Proceedings (2009). http://dx.doi.org/10.46298/dmtcs.2678.

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International audience Given a sequence $(a_k)=a_0,a_1,a_2,\ldots$ of real numbers, define a new sequence $\mathcal{L}(a_k)=(b_k)$ where $b_k=a_k^2-a_{k-1}a_{k+1}$. So $(a_k)$ is log-concave if and only if $(b_k)$ is a nonnegative sequence. Call $(a_k)$ $\textit{infinitely log-concave}$ if $\mathcal{L}^i(a_k)$ is nonnegative for all $i \geq 1$. Boros and Moll conjectured that the rows of Pascal's triangle are infinitely log-concave. Using a computer and a stronger version of log-concavity, we prove their conjecture for the $n$th row for all $n \leq 1450$. We can also use our methods to give a
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3

Narayanan, Hariharan. "Estimating deep Littlewood-Richardson Coefficients." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AT,..., Proceedings (2014). http://dx.doi.org/10.46298/dmtcs.2403.

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International audience Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups $(GL_n)$. The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for Littlewood-Richardson coefficients corresponding to indices sufficiently far from the boundary of the Littlewood Richardson cone. 2. A proof of approximate log-concavity of the above mentioned class of Littlewood-Richardson coefficients. Coefficients de Littlewood Richardson sont des constantes de structure apparaissant dans la théorie de la
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4

Gleitz, Anne-Sophie. "$\ell$-restricted $Q$-systems and quantum affine algebras." Discrete Mathematics & Theoretical Computer Science DMTCS Proceedings vol. AT,..., Proceedings (2014). http://dx.doi.org/10.46298/dmtcs.2375.

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International audience Kuniba, Nakanishi, and Suzuki (1994) have formulated a general conjecture expressing the positive solution of an $\ell$-restricted $Q$-system in terms of quantum dimensions of Kirillov-Reshetikhin modules. After presenting this conjecture, we sketch a proof for the exceptional type $E_6$ following our preprint (2013). In types $E_7$ and $E_8$, we prove positivity for a subset of the nodes of the Dynkin diagram, and we reduce the positivity for the remaining nodes to the conjectural iterated log-concavity of certain explicit sequences of real algebraic numbers. Kuniba, Na
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Dissertations / Theses on the topic "Log-concavité"

1

Bizeul, Pierre. "Stochastic methods in convexity." Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS731.

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Cette thèse s'inscrit dans le cadre des probabilités en grande dimension, en particulier sous hypothèse de convexité. Dans une première partie, on étudie le comportement des l'entropie et de l'information de Fisher vis à vis des convolutions de vecteurs log-concave. Ensuite, à l'aide de la localisation stochastique, une technique récente qui a notamment servi à la quasi résolution de la conjecture KLS, nous établissons des résultats nouveaux sur la fonction de concentration des mesures log-concave, et leur constante de log-sobolev. La dernière partie est consacrée à l'étude de grands systèmes
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