Electronic Communications in Probability

Central Limit Theorems for the Products of Random Matrices Sampled by a Random Walk

Frédérique Duheille-Bienvenue and Nadine Guillotin-Plantard

Full-text: Open access

Abstract

The purpose of the present paper is to study the asymptotic behaviour of the products of random matrices indexed by a random walk following the results obtained by Furstenberg and Kesten (MR0121828) and by Ishitani (MR0438475).

Article information

Source
Electron. Commun. Probab., Volume 8 (2003), paper no. 5, 43-50.

Dates
Accepted: 12 April 2003
First available in Project Euclid: 18 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608889

Digital Object Identifier
doi:10.1214/ECP.v8-1068

Mathematical Reviews number (MathSciNet)
MR1987099

Zentralblatt MATH identifier
1061.60017

Subjects
Primary: 15A52
Secondary: 60G50: Sums of independent random variables; random walks 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J15 60F05: Central limit and other weak theorems

Keywords
Random Walk Random Matrix Random Scenery Functional limit theorem

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Duheille-Bienvenue, Frédérique; Guillotin-Plantard, Nadine. Central Limit Theorems for the Products of Random Matrices Sampled by a Random Walk. Electron. Commun. Probab. 8 (2003), paper no. 5, 43--50. doi:10.1214/ECP.v8-1068. https://projecteuclid.org/euclid.ecp/1463608889


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References

  • BOLTHAUSEN, E., A central limit theorem for two-dimensional random walks in random sceneries, Ann. Probab., (1989), Vol. 17, 108–115.
  • DURRETT, R., Probability: theory and examples, (1991), Wadsworth and Brooks/cole.
  • ERDOS, P., TAYLOR, S.J., Some intersection properties of random walk paths, Acta Math. Acad. Sci. Hungar., (1960), Vol. 11, 231–248.
  • FURSTENBERG, H., KESTEN, H., Products of random matrices, Ann. Math. Statist., (1960), Vol. 31, 457–469.
  • GERL, P., WOESS, W., Local limits and harmonic functions for nonisotropic random walks on free groups, Prob. Theor. Rel. Fields, (1986), Vol. 71, 341–355.
  • ISHITANI, H., A central limit theorem for the subadditive process and its application to products of random matrices, RIMS, Kyoto Univ, (1977), Vol. 12, 565–575.
  • KESTEN, H., Symmetric random walks on groups, Trans. Amer. Math. Soc., (1959), Vol. 92, 336–354.
  • KESTEN, H., SPITZER, F., A limit theorem related to a new class of self-similar processes, Z. Wahrsch. Verw. Gebiete, (1979), Vol. 50, 5–25.
  • SPITZER, F.L., Principles of random walks, (1976), Second Edition, Springer, New York.
  • STONE, C., On local and ratio limit theorems, (1967), Proc. Fifth Berkeley Symp.