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Entropy 2019, 21(3), 312; https://doi.org/10.3390/e21030312

Probability Distributions with Singularities

1
Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
2
INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
3
Dipartimento di Ingegneria, Università della Campania “L. Vanvitelli”, via Roma 29, 81031 Aversa (CE), Italy
*
Author to whom correspondence should be addressed.
Received: 28 February 2019 / Revised: 19 March 2019 / Accepted: 20 March 2019 / Published: 21 March 2019
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Abstract

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. View Full-Text
Keywords: large deviations; phase transitions; condensation of fluctuations; fluctuation relations large deviations; phase transitions; condensation of fluctuations; fluctuation relations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Corberi, F.; Sarracino, A. Probability Distributions with Singularities. Entropy 2019, 21, 312.

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