Skip to main content
SpringerLink
Log in

Hyperfinite spin models

  • Conference paper
  • First Online:
Nonstandard Analysis-Recent Developments

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 983))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. M. Anderson and S. Rashid, A nonstandard characterization of weak convergence. Proc. Amer. Math. Soc., 69(1978), 327–332.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. L. Doob, Stochastic Processes, Wiley, New York, 1953.

    MATH  Google Scholar 

  3. L. Helms, Ergodic properties of several interacting Poisson particles, Adv. in Math., 12(1974), 32–57.

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Helms and P. A. Loeb, Applications of nonstandard analysis to spin models. Jour. of Math. Analysis and Applic., 69(1979), 341–352.

    Article  MathSciNet  MATH  Google Scholar 

  5. T. M. Liggett, Existence theorems for infinite particle systems, Trans. Amer. Math. Soc., 165(1972), 471–481.

    Article  MathSciNet  MATH  Google Scholar 

  6. P. A. Loeb, An Introduction to Nonstandard Analysis and Hyperfinite Probability Theory, in Probabilistic Analysis and Related Topics, A. T. Bharucha-Reid, Ed., Vol. 2, pp. 105–141, Academic Press, 1969.

    Google Scholar 

  7. D. W. Müller, Nonstandard proofs of invariance principles in probability theory, in Applications of Model Theory to Algebra, Analysis, and Probability, W. A. J. Luxemburg, ed., pp. 186–194, Holt, Rinehart and Winston, 1969.

    Google Scholar 

  8. K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York, 1967.

    Book  MATH  Google Scholar 

  9. C. J. Stone, Weak convergence of stochastic processes defined on semi-infinite time intervals, Proc. Amer. Math. Soc., 14(1963), 694–696.

    Article  MathSciNet  MATH  Google Scholar 

  10. D. W. Stroock, Lectures on Infinite Interacting Systems, Kyoto University, Kinokuniya Book-Store Co., Ltd., Tokyo, 1978.

    MATH  Google Scholar 

  11. K. D. Stroyan and W. A. J. Luxemburg, Introduction to the Theory of Infinitesimals, Academic Press, New York, 1976.

    MATH  Google Scholar 

  12. V. A. Volkonskii, Random substitution of time in strong Markov processes, Theory Prob. Appl., 3(1958), 310–325.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Illinois, 61801, Urbana, Illinois

    L. L. Helms

Authors
  1. L. L. Helms
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Albert Emerson Hurd

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Helms, L.L. (1983). Hyperfinite spin models. In: Hurd, A.E. (eds) Nonstandard Analysis-Recent Developments. Lecture Notes in Mathematics, vol 983. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065333

Download citation

  • DOI: https://doi.org/10.1007/BFb0065333

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12279-1

  • Online ISBN: 978-3-540-39602-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation