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Fermions from classical probability and statistics defined by stochastic independence
L. Accardia, Yu. G. Lub a Centro Vito Volterra, Università di Roma Tor Vergata, Roma, Italy
b Dipartimento di Matematica, Università degli Studi di Bari, Bari, Italy
Аннотация:
The case study of fermions and the attempt to deduce their structure from classical probability opens new ways for classical and quantum probability, in particular, for the notion of stochastic coupling which, on the basis of the example of fermions, we enlarge to the notion of algebraic coupling, and for the various notions of stochastic independence. These notions are shown to be strictly correlated with algebraic and stochastic couplings. This approach allows to expand considerably the notion of open system. The above statements will be illustrated with some examples. The last section shows how, from these new stochastic couplings, new statistics emerge alongside the known Maxwell–Boltzmann, Bose–Einstein and Fermi–Dirac statistics.
Bibliography: 5 titles.
Ключевые слова:
fermions, Pauli exclusion principle, stochastic independences, algebraic constraints.
Поступило в редакцию: 12.06.2022 Исправленный вариант: 07.09.2022
Образец цитирования:
L. Accardi, Yu. G. Lu, “Fermions from classical probability and statistics defined by stochastic independence”, Изв. РАН. Сер. матем., 87:5 (2023), 5–40; Izv. Math., 87:5 (2023), 855–890
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/im9389https://doi.org/10.4213/im9389 https://www.mathnet.ru/rus/im/v87/i5/p5
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