Lower bounds for the maximal Lyapunov exponent |
| |
Authors: | Eric S Key |
| |
Institution: | (1) Department of Mathematical Sciences, University of Wisconsin-Milwaukee, 53201 Milwaukee, Wisconsin |
| |
Abstract: | Upper bounds for the maximal Lyapunov exponent,E, of a sequence of matrix-valued random variables are easy to come by asE is the infimum of a real-valued sequence. We shall show that under irreducibility conditions similar to those needed to prove the Perron-Frobenius theorem, one can find sequences which increase toE. As a byproduct of the proof we shall see that we may replace the matrix norm with the spectral radius when computingE in such cases. Finally, a sufficient condition for transience of random walk in a random environment is given. |
| |
Keywords: | Lyapunov exponents nonnegative matrices permanents spectral radius random walk in a random environment |
本文献已被 SpringerLink 等数据库收录! |
|