Discrete versions of the transport equation and the Shepp–Olkin conjecture

E. Hillion; O. T. Johnson

doi:10.1214/14-AOP973

Discrete versions of the transport equation and the Shepp–Olkin conjecture

E. Hillion, O. T. Johnson

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp–Olkin entropy concavity conjecture.

Original language	English
Pages (from-to)	276-306
Number of pages	31
Journal	Annals of Probability
Volume	44
Issue number	1
DOIs	https://doi.org/10.1214/14-AOP973
Publication status	Published - 2 Feb 2016

Bibliographical note

See arxiv:1303.3381

Keywords

entropy
transportation of measures
Bernoulli sums
concavity

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10.1214/14-AOP973

euclid.aop.1454423041
© Institute of Mathematical Statistics, 2016

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1303.3381v2
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Information geometry of graphs
Johnson, O. T. (Principal Investigator)
1/09/11 → 1/09/13
Project: Research

Professor Oliver T Johnson
- O.Johnsonbristol.acuk
- School of Mathematics - Head of School, Professor of Information Theory
- Statistical Science
- Probability, Analysis and Dynamics
Person: Academic , Member, Professional and Administrative

Cite this

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Discrete versions of the transport equation and the Shepp–Olkin conjecture

Abstract

Bibliographical note

Keywords

Access to Document

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Embargoed Document

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Projects

Information geometry of graphs

Profiles

Professor Oliver T Johnson

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