Skip to main content
SpringerLink
Log in

Determinantal Point Processes

  • Chapter
  • First Online:
Reflected Brownian Motions in the KPZ Universality Class

Part of the book series: SpringerBriefs in Mathematical Physics ((BRIEFSMAPHY,volume 18))

  • 722 Accesses

Abstract

Determinantal point processes are the main tool for the study of reflected Brownian motions. Thereby marginal distributions can be expressed in terms of Fredholm determinants, a form which is well suited for an asymptotic analysis. However, only partial aspects of the underlying theory of determinantal point processes is needed for our purposes and we merely introduce the main definitions including the crucial Lemma 3.5. Up to minor modifications, we follow (Johansson 2006) as a very accessible introduction to the topic.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
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

  • K. Johansson, Random matrices and determinantal processes. Math. Stat. Phys. Sess. LXXXIII: Lect. Notes Les Houches Summer Sch. 2005, 1–56 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • B. Simon, Trace Ideals and Their Applications, 2nd edn. (American Mathematical Society, Providence, 2000)

    Google Scholar 

  • B. Eynard, M.L. Mehta, Matrices coupled in a chain. I. Eigenvalue correlations. J. Phys. A 31, 4449–4456 (1998)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • P.J. Forrester, T. Nagao, G. Honner, Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges. Nucl. Phys. B 553, 601–643 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • P.L. Ferrari, H. Spohn, Step fluctations for a faceted crystal. J. Stat. Phys. 113, 1–46 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  • K. Johansson, Discrete polynuclear growth and determinantal processes. Commun. Math. Phys. 242, 277–329 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • A. Borodin, P.L. Ferrari, Large time asymptotics of growth models on space-like paths I: PushASEP. Electron. J. Probab. 13, 1380–1418 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Garching, Germany

    Thomas Weiss

  2. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Patrik Ferrari

  3. Zentrum Mathematik, Technische Universität München, Munich, Germany

    Herbert Spohn

Authors
  1. Thomas Weiss
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrik Ferrari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Herbert Spohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Herbert Spohn .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Author(s)

About this chapter

Cite this chapter

Weiss, T., Ferrari, P., Spohn, H. (2017). Determinantal Point Processes. In: Reflected Brownian Motions in the KPZ Universality Class. SpringerBriefs in Mathematical Physics, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-49499-9_3

Download citation

Publish with us

Policies and ethics

Search

Navigation