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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