Large deviations and localization of the microcanonical ensembles given by multiple constraints

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.

• Publication year

  2018

• Venue

  Annals of Probability

• Publication date

  2018-09-11

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1214/20-aop1430arXiv 1809.04138
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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