Probability Distributions with Singularities

In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism prod...

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Detalles Bibliográficos
Autores principales: Corberi, Federico, Sarracino, Alessandro
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514793/
https://www.ncbi.nlm.nih.gov/pubmed/33267026
http://dx.doi.org/10.3390/e21030312
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author Corberi, Federico
Sarracino, Alessandro
author_facet Corberi, Federico
Sarracino, Alessandro
author_sort Corberi, Federico
collection PubMed
description In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with fluctuation relations.
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spelling pubmed-75147932020-11-09 Probability Distributions with Singularities Corberi, Federico Sarracino, Alessandro Entropy (Basel) Article In this paper we review some general properties of probability distributions which exhibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with fluctuation relations. MDPI 2019-03-21 /pmc/articles/PMC7514793/ /pubmed/33267026 http://dx.doi.org/10.3390/e21030312 Text en © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Corberi, Federico
Sarracino, Alessandro
Probability Distributions with Singularities
title Probability Distributions with Singularities
title_full Probability Distributions with Singularities
title_fullStr Probability Distributions with Singularities
title_full_unstemmed Probability Distributions with Singularities
title_short Probability Distributions with Singularities
title_sort probability distributions with singularities
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7514793/
https://www.ncbi.nlm.nih.gov/pubmed/33267026
http://dx.doi.org/10.3390/e21030312
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AT sarracinoalessandro probabilitydistributionswithsingularities

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