Skip to main content
SpringerLink
Log in

Large Deviation Preliminaries

  • Chapter
  • First Online:
Book cover Large Deviations for Random Graphs

Part of the book series: Lecture Notes in Mathematics ((LNMECOLE,volume 2197))

  • 2205 Accesses

Abstract

This chapter contains some basic definitions and results from abstract large deviation theory. As before, no background other than graduate-level probability and functional analysis is required, and the discussion is limited to the minimum required for the monograph.

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 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

References

  1. Azuma, K. (1967). Weighted sums of certain dependent random variables. Tohoku Mathematical Journal, Second Series, 19(3), 357–367.

    Article  MathSciNet  MATH  Google Scholar 

  2. de Acosta, A. (1985). Upper bounds for large deviations of dependent random vectors. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 69, 551–565.

    Article  MathSciNet  MATH  Google Scholar 

  3. Dembo, A., & Zeitouni, O. (2010). Large deviations techniques and applications. Corrected reprint of the second (1998) edition. Berlin: Springer.

    Google Scholar 

  4. Gärtner, J. (1977). On large deviations from the invariant measure. Theory of Probablity and its Applications, 22, 24–39.

    Article  MathSciNet  MATH  Google Scholar 

  5. Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58, 13–30.

    Article  MathSciNet  MATH  Google Scholar 

  6. McDiarmid, C. (1989). On the method of bounded differences. In J. Siemons (Ed.), Surveys in combinatorics. London Mathematical Society Lecture Notes Series, vol. 141, pp. 148–188. Cambridge: Cambridge University Press.

    Google Scholar 

  7. Shamir, E., & Spencer, J. (1987). Sharp concentration of the chromatic number on random graphs G n, p . Combinatorica, 7(1), 121–129.

    Google Scholar 

  8. Stroock, D. W. (1984). An introduction to the theory of large deviations. Berlin: Springer.

    Book  MATH  Google Scholar 

  9. Varadhan, S. R. S. (1966). Asymptotic probabilities and differential equations. Communications on Pure and Applied Mathematics, 19, 261–286.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Stanford University, Stanford, CA, USA

    Sourav Chatterjee

Authors
  1. Sourav Chatterjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Chatterjee, S. (2017). Large Deviation Preliminaries. In: Large Deviations for Random Graphs. Lecture Notes in Mathematics(), vol 2197. Springer, Cham. https://doi.org/10.1007/978-3-319-65816-2_4

Download citation

Publish with us

Policies and ethics

Search

Navigation