### Abstract

It is shown that the product of the Rényi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santaló inequality).

Original language | English (US) |
---|---|

Pages (from-to) | 757-774 |

Number of pages | 18 |

Journal | Annals of Probability |

Volume | 32 |

Issue number | 1 B |

State | Published - Jan 2004 |

### Fingerprint

### Keywords

- Blaschke-Santaló inequality
- Dual mixed volumes
- Rényi entropy

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Annals of Probability*,

*32*(1 B), 757-774.

**Moment-entropy inequalities.** / Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 32, no. 1 B, pp. 757-774.

}

TY - JOUR

T1 - Moment-entropy inequalities

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

PY - 2004/1

Y1 - 2004/1

N2 - It is shown that the product of the Rényi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santaló inequality).

AB - It is shown that the product of the Rényi entropies of two independent random vectors provides a sharp lower bound for the expected value of the moments of the inner product of the random vectors. This new inequality contains important geometry (such as extensions of one of the fundamental affine isoperimetric inequalities, the Blaschke-Santaló inequality).

KW - Blaschke-Santaló inequality

KW - Dual mixed volumes

KW - Rényi entropy

UR - http://www.scopus.com/inward/record.url?scp=2142806971&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2142806971&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:2142806971

VL - 32

SP - 757

EP - 774

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 1 B

ER -