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dc.contributor.author
Zanette, Damian Horacio
dc.contributor.author
Samengo, Ines
dc.date.available
2024-03-21T13:12:56Z
dc.date.issued
2024-01
dc.identifier.citation
Zanette, Damian Horacio; Samengo, Ines; The Emergence of the Normal Distribution in Deterministic Chaotic Maps; Molecular Diversity Preservation International; Entropy; 26; 1; 1-2024; 1-18
dc.identifier.issn
1099-4300
dc.identifier.uri
http://hdl.handle.net/11336/231153
dc.description.abstract
The central limit theorem states that, in the limits of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to attain a stable distribution. The condition of independence, however, only holds in real systems as an approximation. To extend the theorem to more general situations, previous studies have derived a version of the central limit theorem that also holds for variables that are not independent. Here, we present numerical results that characterize how convergence is attained when the variables being summed are deterministically related to one another through the recurrent application of an ergodic mapping. In all the explored cases, the convergence to the limit distribution is slower than for random sampling. Yet, the speed at which convergence is attained varies substantially from system to system, and these variations imply differences in the way information about the deterministic nature of the dynamics is progressively lost as the number of summands increases. Some of the identified factors in shaping the convergence process are the strength of mixing induced by the mapping and the shape of the marginal distribution of each variable, most particularly, the presence of divergences or fat tails.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Molecular Diversity Preservation International
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
STABLE DISTRIBUTIONS
dc.subject
DETERMINISTIC SYSTEMS
dc.subject
CENTRAL LIMIT THEOREM
dc.subject.classification
Otras Ciencias Físicas
dc.subject.classification
Ciencias Físicas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
The Emergence of the Normal Distribution in Deterministic Chaotic Maps
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-03-19T14:27:22Z
dc.journal.volume
26
dc.journal.number
1
dc.journal.pagination
1-18
dc.journal.pais
Suiza
dc.journal.ciudad
Basel
dc.description.fil
Fil: Zanette, Damian Horacio. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.description.fil
Fil: Samengo, Ines. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
dc.journal.title
Entropy
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/26/1/51
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.3390/e26010051
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