Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-08T19:20:59.888Z Has data issue: false hasContentIssue false
  • English
  • Français

L'application des representations au calcul explicite sur certaines chaînes de Markov finies

Published online by Cambridge University Press:  01 July 2016

Bernard Ycart
Bernard Ycart*
Affiliation:
Université Paul Sabatier, Toulouse
*
∗Adresse postale: Laboratoire de Statistique et Probabilités, ERA-CNRS 591, Université Paul Sabatier, 31062 Toulouse Cedex, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

We give here concrete formulas relating the transition generatrix functions of any random walk on a finite group to the irreducible representations of this group. Some examples of such explicit calculations for the permutation groups A4, S4, and A5 are included.

Keywords

RANDOM WALKS ON FINITE GROUPSGROUP REPRESENTATIONS
Type
Research Article
Information
Advances in Applied Probability , Volume 16 , Issue 3 , September 1984 , pp. 656 - 666
Copyright
Copyright © Applied Probability Trust 1984 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bibliographie

Burrow, M. (1965) Representation Theory of Finite Groups. Academic Press, New York.CrossRefGoogle Scholar
Feller, W. (1950) An Introduction to Probability Theory and its Applications, Vol. 1. Wiley, New York.Google Scholar
Frobenius, F. G. (1969) Gesammelte Abhandlungen, Bd III. Springer-Verlag, Berlin.Google Scholar
Godement, R. (1966) Cours d'algèbre. Hermann, Paris.Google Scholar
Hannan, E. J. (1965) Group representations and applied probability. J. Appl. Prob. 2, 1–68.Google Scholar
Hawkins, T. H. (1978) The creation of the theory of group characters. In History of Analysis. Rice University Studies 64, Houston, Texas.Google Scholar
Heyer, H. (1977) Probability Measures on Locally Compact Groups. Springer-Verlag, Berlin.Google Scholar
Letac, G. (1981) Problèmes classiques de probabilité sur un couple de Gelfand. In Analytic Methods in Probability Theory. Lecture Notes in Mathematics 861, Springer-Verlag, Berlin.Google Scholar
Letac, G. (1982) Les fonctions sphériques d'un couple de Gelfand symétrique et les chaînes de Markov. Adv. Appl. Prob. 14, 272–294.Google Scholar
Letac, G. and Takacs, L. (1979) Random walks on the m-dimensional cube. J. Reine Angew. Math. 310, 178–185.Google Scholar
Letac, G. and Takacs, L. (1980a) Random walks on a dodecahedron. J. Appl. Prob. 17, 373–384.Google Scholar
Letac, G. and Takacs, L. (1980b) Random walks on the 600-cell polyhedron. SIAM J. Algebraic and Discrete Math. 1, 114–123.Google Scholar
Serre, J. P. (1978) Représentations linéaires des groupes finis. Hermann, Paris.Google Scholar
Takacs, L. (1982) Random walks on groups. Linear Algebra Appl. 43, 49–67.CrossRefGoogle Scholar