Results 11 to 20 of about 6,495 (249)
Negative correlation and log‐concavity [PDF]
Random Structures & Algorithms, 2009 AbstractWe give counterexamples and a few positive results related to several conjectures of R. Pemantle (Pemantle, J Math Phys 41 (2000), 1371–1390) and D. Wagner (Wagner, Ann Combin 12 (2008), 211–239) concerning negative correlation and log‐concavity properties for probability measures and relations between them.
Kahn, J., Neiman, M.
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Optimal $L^2$ Extensions of Openness Type and Related Topics
Comptes Rendus. Mathématique, 2023 We establish several optimal $L^2$ extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal $L^2$ extensions, which generalizes the product property of Bergman kernels.
Xu, Wang, Zhou, Xiangyu
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Equivariant Log Concavity and Representation Stability [PDF]
International Mathematics Research Notices, 2021 AbstractWe expand upon the notion of equivariant log concavity and make equivariant log concavity conjectures for Orlik–Solomon algebras of matroids, Cordovil algebras of oriented matroids, and Orlik–Terao algebras of hyperplane arrangements. In the case of the Coxeter arrangement for the Lie algebra $\mathfrak{s}\mathfrak{l}_n$, we exploit the theory ...
Matherne, J. +3 more
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The ratio log-concavity of the Cohen numbers
Journal of Inequalities and Applications, 2016 Let U n $U_{n}$ denote the nth Cohen number. Some combinatorial properties for U n $U_{n}$ have been discovered. In this paper, we prove the ratio log-concavity of U n $U_{n}$ by establishing the lower and upper bounds for U n U n − 1 $\frac{U_{n}}{U_{n ...
Eric H Liu, Lily J Jin
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Proof of a conjecture of Z-W Sun on ratio monotonicity
Journal of Inequalities and Applications, 2016 In this paper, we study the log-behavior of a new sequence { S n } n = 0 ∞ $\{S_{n}\} _{n=0}^{\infty}$ , which was defined by Z-W Sun. We find that the sequence is log-convex by using the interlacing method.
Brian Yi Sun +2 more
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Risks, 2023 Log-concavity and log-convexity play a key role in various scientific fields, especially in those where the distinction between exponential and non-exponential distributions is necessary for inferential purposes.
Alex Karagrigoriou +3 more
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Log-concavity of characteristic polynomials and the Bergman fan of matroids [PDF]
, 2012 In a recent paper, the first author proved the log-concavity of the coefficients of the characteristic polynomial of a matroid realizable over a field of characteristic 0, answering a long-standing conjecture of Read in graph theory.
Huh, June, Katz, Eric
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Valuations on Log-Concave Functions [PDF]
The Journal of Geometric Analysis, 2020 A classification of $\operatorname{SL}(n)$ and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as $\operatorname{SL}(n)$ and ...
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Estimating deep Littlewood-Richardson Coefficients [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 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.
Hariharan Narayanan
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Chernoff’s density is log-concave
Bernoulli, 2014 We show that the density of $Z=\mathop {\operatorname {argmax}}\{W(t)-t^2\}$, sometimes known as Chernoff's density, is log-concave. We conjecture that Chernoff's density is strongly log-concave or "super-Gaussian", and provide evidence in support of the conjecture.
Balabdaoui, Fadoua, Wellner, Jon
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