Large deviations and Chernoff bound for certain correlated states on a spin chain

Fumio Hiai, M. Mosonyi, Tomohiro Ogawa

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

In this paper we extend the results of Lenci and Rey-Bellet [J. Stat. Phys. 119, 715 (2005)] on the large deviation upper bound of the distribution measures of local Hamiltonians with respect to a Gibbs state in the setting of translation-invariant finite-range interactions. We show that a certain factorization property of the reference state is sufficient for a large deviation upper bound to hold and that this factorization property is satisfied by Gibbs states of the above kind as well as finitely correlated states. As an application of the methods, the Chernoff bound for correlated states with factorization property is studied. In the specific case of the distributions of the ergodic averages of a one-site observable with respect to an ergodic finitely correlated state, the spectral theory of positive maps is applied to prove the full large deviation principle.

Original languageEnglish
Article number123301
JournalJournal of Mathematical Physics
Volume48
Issue number12
DOIs
Publication statusPublished - 2007

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Spin Chains
Large Deviations
factorization
Factorization
Gibbs States
deviation
spectral theory
Upper bound
Ergodic Averages
Large Deviation Principle
Spectral Theory
Sufficient
Invariant
Interaction
Range of data
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Large deviations and Chernoff bound for certain correlated states on a spin chain. / Hiai, Fumio; Mosonyi, M.; Ogawa, Tomohiro.

In: Journal of Mathematical Physics, Vol. 48, No. 12, 123301, 2007.

Research output: Contribution to journalArticle

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