Distinguishability notion based on Wootters statistical distance : Application to discrete maps

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We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitr...

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Autores principales:	Gómez, Ignacio Sebastián, Portesi, Mariela Adelina, Lamberti, Pedro Walter
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2017
Materias:	Astronomía Física Distinguishability Statistical distance Discrete maps
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/97900 https://ri.conicet.gov.ar/11336/65842 https://aip.scitation.org/doi/10.1063/1.4998141
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-97900
record_format	dspace
institution	Universidad Nacional de La Plata
institution_str	I-19
repository_str	R-120
collection	SEDICI (UNLP)
language	Inglés
topic	Astronomía Física Distinguishability Statistical distance Discrete maps
spellingShingle	Astronomía Física Distinguishability Statistical distance Discrete maps Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter Distinguishability notion based on Wootters statistical distance : Application to discrete maps
topic_facet	Astronomía Física Distinguishability Statistical distance Discrete maps
description	We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d for an arbitrary discrete map. Moreover, from d, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.
format	Articulo Articulo
author	Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter
author_facet	Gómez, Ignacio Sebastián Portesi, Mariela Adelina Lamberti, Pedro Walter
author_sort	Gómez, Ignacio Sebastián
title	Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_short	Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_full	Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_fullStr	Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_full_unstemmed	Distinguishability notion based on Wootters statistical distance : Application to discrete maps
title_sort	distinguishability notion based on wootters statistical distance : application to discrete maps
publishDate	2017
url	http://sedici.unlp.edu.ar/handle/10915/97900 https://ri.conicet.gov.ar/11336/65842 https://aip.scitation.org/doi/10.1063/1.4998141
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bdutipo_str	Repositorios
_version_	1764820492460490755

Distinguishability notion based on Wootters statistical distance : Application to discrete maps

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