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On concentration properties of disordered Hamiltonians


Authors: Antonio Auffinger and Wei-Kuo Chen
Journal: Proc. Amer. Math. Soc. 146 (2018), 1807-1815
MSC (2010): Primary 60K35, 60G15, 82B44
DOI: https://doi.org/10.1090/proc/13864
Published electronically: January 12, 2018
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Abstract: We present an elementary approach to concentration of disordered Hamiltonians. Assuming differentiability of the limiting free energy $ F$ with respect to the inverse temperature $ \beta $, we show that the Hamiltonian concentrates around the energy level $ F'(\beta )$ under the free energy and Gibbs average.


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Additional Information

Antonio Auffinger
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
Email: auffing@math.northwestern.edu

Wei-Kuo Chen
Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, Minnesota 55455
Email: wkchen@umn.edu

DOI: https://doi.org/10.1090/proc/13864
Received by editor(s): February 28, 2017
Received by editor(s) in revised form: June 17, 2017
Published electronically: January 12, 2018
Communicated by: Zhen-Qing Chen
Article copyright: © Copyright 2018 American Mathematical Society

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