LARGE DEVIATIONS AND LOCALIZATION OF THE MICROCANONICAL ENSEMBLES GIVEN BY MULTIPLE CONSTRAINTS

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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.
Publisher
INST MATHEMATICAL STATISTICS-IMS
Issue Date
2020-09
Language
English
Article Type
Article
Citation

ANNALS OF PROBABILITY, v.48, no.5, pp.2525 - 2564

ISSN
0091-1798
DOI
10.1214/20-AOP1430
URI
http://hdl.handle.net/10203/287559
Appears in Collection
MA-Journal Papers(저널논문)
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