A representation of the moment measures of the general ideal Boe gas

Nehring B, Zessin HN (2012)
Mathematische Nachrichten 285(7): 878-888.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Nehring, Benjamin; Zessin, Hans NorbertUniBi
Abstract / Bemerkung
We reconsider the fundamental work of Fichtner 2 and exhibit the permanental structure of the ideal Bose gas again, using a new approach which combines a characterization of infinitely divisible random measures (due to Kerstan, Kummer and Matthes 4, 6 and Mecke 9, 10) with a decomposition of the moment measures into its factorial measures due to Krickeberg 5. To be more precise, we exhibit the moment measures of all orders of the general ideal Bose gas in terms of certain loop integrals. This representation can be considered as a point process analogue of the old idea of Symanzik 15 that local times and self-crossings of the Brownian motion can be used as a tool in quantum field theory. Behind the notion of a general ideal Bose gas there is a class of infinitely divisible point processes of all orders with a Levy-measure belonging to some large class of measures containing that of the classical ideal Bose gas considered by Fichtner. It is well-known that the calculation of moments of higher order of point processes is notoriously complicated. See for instance Krickebergs calculations for the Poisson or the Cox process in 5. Relations to the work of Shirai, Takahashi 12 and Soshnikov 14 on permanental and determinantal processes are outlined.
Stichworte
2010) 35K55; 35K65; integration by parts formula; Infinitely divisible point processes; random KMM-measure; permanental and determinantal point processes (MSC
Erscheinungsjahr
2012
Zeitschriftentitel
Mathematische Nachrichten
Band
285
Ausgabe
7
Seite(n)
878-888
ISSN
0025-584X
Page URI
https://pub.uni-bielefeld.de/record/2501684

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Nehring B, Zessin HN. A representation of the moment measures of the general ideal Boe gas. Mathematische Nachrichten. 2012;285(7):878-888.
Nehring, B., & Zessin, H. N. (2012). A representation of the moment measures of the general ideal Boe gas. Mathematische Nachrichten, 285(7), 878-888. doi:10.1002/mana.201000111
Nehring, B., and Zessin, H. N. (2012). A representation of the moment measures of the general ideal Boe gas. Mathematische Nachrichten 285, 878-888.
Nehring, B., & Zessin, H.N., 2012. A representation of the moment measures of the general ideal Boe gas. Mathematische Nachrichten, 285(7), p 878-888.
B. Nehring and H.N. Zessin, “A representation of the moment measures of the general ideal Boe gas”, Mathematische Nachrichten, vol. 285, 2012, pp. 878-888.
Nehring, B., Zessin, H.N.: A representation of the moment measures of the general ideal Boe gas. Mathematische Nachrichten. 285, 878-888 (2012).
Nehring, Benjamin, and Zessin, Hans Norbert. “A representation of the moment measures of the general ideal Boe gas”. Mathematische Nachrichten 285.7 (2012): 878-888.

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