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Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees

  • Sander Dommers
  • Cristian Giardinà
  • Claudio Giberti
  • Remco van der Hofstad
Article
  • 36 Downloads

Abstract

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.

Keywords

Random graphs Ising model Annealing Large deviations 

Notes

Acknowledgements

Sander Dommers has been supported by the Deutsche Forschungsgemeinschaft (DFG) via RTG 2131 High-dimensional Phenomena in Probability – Fluctuations and Discontinuity. We acknowledge financial support from the Italian Research Funding Agency (MIUR) through FIRB project “Stochastic processes in interacting particle systems: duality, metastability and their applications”, Grant No. RBFR10N90W. The work of Remco van der Hofstad is supported in part by the Netherlands Organisation for Scientific Research (NWO) through VICI Grant 639.033.806 and the Gravitation Networks Grant 024.002.003. C. Giberti and C. Giardinà acknowledge financial supports from “Fondo di Ateneo per la Ricerca 2015” and “Fondo di Ateneo per la Ricerca 2016”, Università di Modena e Reggio Emilia.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ruhr-University BochumBochumGermany
  2. 2.University of Modena and Reggio EmiliaModenaItaly
  3. 3.University of Modena and Reggio EmiliaReggio EmiliaItaly
  4. 4.Eindhoven University of TechnologyEindhovenThe Netherlands

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