Products of random matrices: Dimension and growth in norm

Kargin, Vladislav

Ann. Appl. Probab., Tome 20 (2010) no. 1, p. 890-906 / Harvested from Project Euclid

Résumé

Suppose that X₁, …, X_n, … are i.i.d. rotationally invariant N-by-N matrices. Let Π_n=X_n⋯X₁. It is known that n⁻¹log |Π_n| converges to a nonrandom limit. We prove that under certain additional assumptions on matrices X_i the speed of convergence to this limit does not decrease when the size of matrices, N, grows.

Publié le : 2010-06-15
Classification: Random matrices, Furstenberg–Kesten theorem, 15A52, 60B10

@article{1276867301,
     author = {Kargin, Vladislav},
     title = {Products of random matrices: Dimension and growth in norm},
     journal = {Ann. Appl. Probab.},
     volume = {20},
     number = {1},
     year = {2010},
     pages = { 890-906},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1276867301}
}

Kargin, Vladislav. Products of random matrices: Dimension and growth in norm. Ann. Appl. Probab., Tome 20 (2010) no. 1, pp.  890-906. http://gdmltest.u-ga.fr/item/1276867301/