Skip to main content
SpringerLink
Log in

Shabat polynomials and harmonic measure

  • Chapter
  • First Online:
Séminaire de Probabilités XLII

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 1979))

Abstract

This note is inspired by [BZ], which describes the true shape of a tree. Each planar tree (remember that a planar tree is a tree in which, for each vertex, the adjacent edges are cyclically ordered) has a distinguished embedding in the complex plane (up to similitude).

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Bétréma, J., Zvonkin, A.: La vraie forme d'un arbre. TAPSOFT '93: theory and practice of software development (Orsay, 1993), 599–612, Lecture Notes in Comput. Sci., 668, Springer, Berlin, 1993. 05C05.

    Google Scholar 

  2. Doob, J.L.: Classical potential theory and its probabilistic counterpart. Grundlehren der Mathematischen Wissenschaften, 262. Springer-Verlag, New York, 1984.

    Google Scholar 

  3. Lando, S., Zvonkin, A.: Graphs on surfaces and their applications, Encyclopedia of Mathematical Sciences, Low dimensional topology, II. Springer-Verlag, berlin, Heidelberg, 2004.

    Google Scholar 

  4. Marshall, D.E.; Rohde, S.: The Löwner differential equation and slit mappings. J. Amer. Math. Soc. 18 (2005), no. 4, 763–778.

    Article  MathSciNet  MATH  Google Scholar 

  5. Rudin, W.: Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS , Laboratoire d’Informatique Institut Gaspard Monge Université Paris-Est, 5 bd Descartes, 77454, Champs-sur-Marne, Marne-la-Vallée, cedex 2

    Philippe Biane

Authors
  1. Philippe Biane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philippe Biane .

Editor information

Editors and Affiliations

  1. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. Inst. Recherche, Mathématiques Avancées, Université Strasbourg I, rue René Descartes 7, Strasbourg CX, 67084, France

    Michel Émery

  3. Laboratoire de Mathematiques, Université de Versailles, av. des Etats-Unis 45, Versailles CX, 78035, France

    Alain Rouault

  4. CNRS UMR 6623, Lab. de Mathématiques, Université Besancon, route de Gray 16, Besancon CX, 25030, France

    Christophe Stricker

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Biane, P. (2009). Shabat polynomials and harmonic measure. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLII. Lecture Notes in Mathematics(), vol 1979. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01763-6_5

Download citation

Publish with us

Policies and ethics

Search

Navigation