Skip to main content
SpringerLink
Log in

No cut-off phenomenon for the “Insect Markov chain”

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

In this work we show that the probability measure associated with the Insect Markov chain defined on the ultrametric space of the leaves of the q-ary rooted tree of depth n ≥ 2 converges to the stationary distribution without a cut-off behavior.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aldous D., Diaconis P.: Shuffling cards and stopping times. Am. Math. Monthly 93, 333–348 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ceccherini-Silberstein T., Scarabotti F., Tolli F.: Finite Gelfand pairs and their applications to probability and statistics. J. Math. Sci. NY. 141(2), 1182–1229 (2007)

    Article  MathSciNet  Google Scholar 

  3. Ceccherini-Silberstein, T., Scarabotti, F., Tolli, F.: Harmonic analysis on finite groups: representation theory, Gelfand Pairs and Markov chains. In: Cambridge Studies in Advanced Mathematics, vol. 108. Cambridge University Press, Cambridge (2008)

  4. D’Angeli, D., Donno, A.: Crested products of Markov chains. Ann. Appl. Probab. (accepted) (2008)

  5. Diaconis P.: The cut-off phenomenon in finite Markov chains. Proc. Nat. Acad. Sci. USA. 93, 1659–1664 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Diaconis P., Saloff-Coste L.: Separation cut-offs for birth and death chains. Ann. Appl. Probab. 16, 2098–2122 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Figà-Talamanca, A.: An application of Gelfand pairs to a problem of diffusion in compact ultrametric spaces. In: Topics in Probability and Lie Groups: Boundary Theory, CRM Proc. Lecture Notes, vol. 28, Am. Math. Soc. Providence, RI, pp. 51–67 (2001)

Download references

Author information

Authors and Affiliations

  1. Section de Mathématiques, Université de Genève, 2-4, Rue du Lièvre, Case Postale 64, 1211, Geneva 4, Switzerland

    Daniele D’Angeli & Alfredo Donno

Authors
  1. Daniele D’Angeli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfredo Donno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniele D’Angeli.

Additional information

Communicated by D. Elworthy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

D’Angeli, D., Donno, A. No cut-off phenomenon for the “Insect Markov chain”. Monatsh Math 156, 201–210 (2009). https://doi.org/10.1007/s00605-008-0014-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00605-008-0014-x

Keywords

Mathematics Subject Classification (2000)

Search

Navigation