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A de Finetti-type theorem withm-dependent states
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  • Published: March 1990

A de Finetti-type theorem withm-dependent states

  • Dénes Petz1 

Probability Theory and Related Fields volume 85, pages 65–72 (1990)Cite this article

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Summary

In this paper certain translation invariant states on the infinite tensor productC *-algebra

are considered. Form ∈ ℤ+ a state ϕ onA ism-dependent if

$$\varphi (a_1 \otimes a_2 \otimes ... \otimes a_l ) = \varphi (a_1 \otimes ... \otimes a_k )\varphi (a_{k + m + 1} \otimes ... \otimes a_l )$$

wheneverl>k+m anda k + 1 =a k + 2 = ... =a k +m = 1. The closed convex hull of the stationarym-dependent states is characterized by a symmetry condition. The case ofm=0 corresponds to independence and the result reduces to aC *-algebraic version, due to E. Størmer, of the classical de Finetti's theorem on exchangeable sequences.

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References

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Author information

Authors and Affiliations

  1. Instituut voor Theoretische Fysica, Universiteit Leuven, B-3030, Leuven, Belgium

    Dénes Petz

Authors
  1. Dénes Petz
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Additional information

Partially supported by the Hungarian National Foundations for Scientific Research grant no. 1816. On leave of absence from the Mathematical Institute HAS, Budapest

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Petz, D. A de Finetti-type theorem withm-dependent states. Probab. Th. Rel. Fields 85, 65–72 (1990). https://doi.org/10.1007/BF01377629

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  • Received: 16 February 1989

  • Revised: 01 September 1989

  • Issue Date: March 1990

  • DOI: https://doi.org/10.1007/BF01377629

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Keywords

  • Hull
  • Stochastic Process
  • Probability Theory
  • Convex Hull
  • Mathematical Biology
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