Remarks about mixed discriminants and volumes

S. Artstein-Avidan; D. Florentin; Y. Ostrover

doi:https://doi.org/10.1142/S0219199713500314

Remarks about mixed discriminants and volumes

S. Artstein-Avidan, D. Florentin, Y. Ostrover

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in ℝⁿ. Moreover, we discuss how the latter are related to the monotonicity of an information functional on the class of convex bodies, which is a geometric analogue of the classical Fisher information.

Original language	English
Article number	1350031
Journal	Communications in Contemporary Mathematics
Volume	16
Issue number	2
DOIs	https://doi.org/10.1142/S0219199713500314
State	Published - Apr 2014

Keywords

Mixed volumes
convex bodies
mixed discriminants
monotonicity of information
zonoids

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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https://doi.org/10.1142/S0219199713500314

Cite this

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title = "Remarks about mixed discriminants and volumes",

abstract = "In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in ℝn. Moreover, we discuss how the latter are related to the monotonicity of an information functional on the class of convex bodies, which is a geometric analogue of the classical Fisher information.",

keywords = "Mixed volumes, convex bodies, mixed discriminants, monotonicity of information, zonoids",

author = "S. Artstein-Avidan and D. Florentin and Y. Ostrover",

note = "Funding Information: We thank Prof. R. Schneider for his comments on the written text. The first and second-named authors were partially supported by ISF grant No. 247/11. The third-named author was partially supported by a Reintegration Grant SSGHD-268274 within the 7th European community framework programme, and by ISF grant No. 1057/10.",

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AU - Artstein-Avidan, S.

AU - Florentin, D.

AU - Ostrover, Y.

N1 - Funding Information: We thank Prof. R. Schneider for his comments on the written text. The first and second-named authors were partially supported by ISF grant No. 247/11. The third-named author was partially supported by a Reintegration Grant SSGHD-268274 within the 7th European community framework programme, and by ISF grant No. 1057/10.

PY - 2014/4

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N2 - In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in ℝn. Moreover, we discuss how the latter are related to the monotonicity of an information functional on the class of convex bodies, which is a geometric analogue of the classical Fisher information.

AB - In this note we prove certain inequalities for mixed discriminants of positive semi-definite matrices, and mixed volumes of compact convex sets in ℝn. Moreover, we discuss how the latter are related to the monotonicity of an information functional on the class of convex bodies, which is a geometric analogue of the classical Fisher information.

KW - Mixed volumes

KW - convex bodies

KW - mixed discriminants

KW - monotonicity of information

KW - zonoids

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DO - https://doi.org/10.1142/S0219199713500314

M3 - مقالة

SN - 0219-1997

VL - 16

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 2

M1 - 1350031

ER -

Remarks about mixed discriminants and volumes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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