A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-c...

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Main Authors:	Stéphane Chrétien, Juan-Pablo Ortega
Format:	Article
Language:	English
Published:	MDPI AG 2018-03-01
Series:	Mathematics
Subjects:	dynamical systems Hilbert metric Liverani’s formula
Online Access:	http://www.mdpi.com/2227-7390/6/3/35

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spelling	doaj-ee156e29a91b4c54918bcebac59745382020-11-24T20:54:22ZengMDPI AGMathematics2227-73902018-03-01633510.3390/math6030035math6030035A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian ConeStéphane Chrétien0Juan-Pablo Ortega1National Physical Laboratory, Hampton Road, Teddinton TW11 0LW, UKFaculty of Mathematics and Statistics, University of St. Gallen, CH-9000 St. Gallen, SwitzerlandThe Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-compact and multidimensional setting with a different cone, taylored for sub-Gaussian tails.http://www.mdpi.com/2227-7390/6/3/35dynamical systemsHilbert metricLiverani’s formula
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Stéphane Chrétien Juan-Pablo Ortega
spellingShingle	Stéphane Chrétien Juan-Pablo Ortega A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone Mathematics dynamical systems Hilbert metric Liverani’s formula
author_facet	Stéphane Chrétien Juan-Pablo Ortega
author_sort	Stéphane Chrétien
title	A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone
title_short	A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone
title_full	A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone
title_fullStr	A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone
title_full_unstemmed	A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone
title_sort	simple formula for the hilbert metric with respect to a sub-gaussian cone
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2018-03-01
description	The Hilbert metric is a widely used tool for analysing the convergence of Markov processes and the ergodic properties of deterministic dynamical systems. A useful representation formula for the Hilbert metric was given by Liverani. The goal of the present paper is to extend this formula to the non-compact and multidimensional setting with a different cone, taylored for sub-Gaussian tails.
topic	dynamical systems Hilbert metric Liverani’s formula
url	http://www.mdpi.com/2227-7390/6/3/35
work_keys_str_mv	AT stephanechretien asimpleformulaforthehilbertmetricwithrespecttoasubgaussiancone AT juanpabloortega asimpleformulaforthehilbertmetricwithrespecttoasubgaussiancone AT stephanechretien simpleformulaforthehilbertmetricwithrespecttoasubgaussiancone AT juanpabloortega simpleformulaforthehilbertmetricwithrespecttoasubgaussiancone
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A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone

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