Goldschmidt, C. (Christina), Ueltschi, Daniel and Windridge, Peter (2011) Quantum Heisenberg models and their probability representations. In: Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Contemporary mathematics, Vol.552 . American Mathematical Society, Providence, R.I., pp. 177-224. ISBN 9780821868980

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Abstract

These notes give a mathematical introduction to two seemingly unrelated topics: (i) quantum spin systems and their cycle and loop representations, due to Toth and Aizenman-Nachtergaele; (ii) coagulation-fragmentation stochastic processes. These topics are nonetheless related, as we argue that the lengths of cycles and loops satisfy an effective coagulation-fragmentation process. This suggests that their joint distribution is Poisson-Dirichlet. These ideas are far from being proved, but they are backed by several rigorous results, notably of Dyson-Lieb-Simon and Schramm.

Item Type:	Book Item
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Series Name:	Contemporary mathematics
Publisher:	American Mathematical Society
Place of Publication:	Providence, R.I.
ISBN:	9780821868980
Book Title:	Entropy and the quantum II : Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona
Editor:	Sims, Robert and Ueltschi, Daniel
Date:	2011
Volume:	Vol.552
Number of Pages:	224
Page Range:	pp. 177-224
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/44228

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