Open Access
September 2020 Large deviations and localization of the microcanonical ensembles given by multiple constraints
Kyeongsik Nam
Ann. Probab. 48(5): 2525-2564 (September 2020). DOI: 10.1214/20-AOP1430


We develop a unified theory to analyze the microcanonical ensembles with several constraints given by unbounded observables. Several interesting phenomena that do not occur in the single constraint case can happen under the multiple constraints case. We systematically analyze the detailed structures of such microcanonical ensembles in two orthogonal directions using the theory of large deviations. First of all, we establish the equivalence of ensembles result, which exhibits an interesting phase transition phenomenon. Secondly, we study the localization and delocalization phenomena by obtaining large deviation results for the joint law of empirical distributions and the maximum component. Some concrete examples for which the theory applies will be given as well.


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Kyeongsik Nam. "Large deviations and localization of the microcanonical ensembles given by multiple constraints." Ann. Probab. 48 (5) 2525 - 2564, September 2020.


Received: 1 February 2019; Revised: 1 February 2020; Published: September 2020
First available in Project Euclid: 23 September 2020

MathSciNet: MR4152650
Digital Object Identifier: 10.1214/20-AOP1430

Primary: 60F10 , 82B05 , 82B26

Keywords: equivalence of ensembles , large deviation principle , Localization , microcanonical ensembles , phase transition

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 5 • September 2020
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