Seminari del Dipartimento
Fisica Matematica Singular behavior of the Lyapunov exponent of a product of random 2x2 matrices Rafael Greenblatt 28-03-2017 - 14:30 AULA 311 (SEMINARI) Largo San L. Murialdo,1
We consider a certain infinite product of random 2x2 matrices appearing in the exact solution of some 1 and 1+1 dimensional disordered models in statistical mechanics, which depends on a deterministic real parameter $epsilon$ and a random real parameter with distribution $mu$. For a large class of $mu$, we prove a prediction by B. Derrida and H. J. Hillhorst (1983) that the Lyapunov exponent behaves like $Cepsilon^{2 alpha}$ in the limit $epsilon o 0$, where $alpha in (0,1)$ is determined by $mu$. The proof is made possible by a contractivity argument which makes it possible to explicitly control the error involved in using an approximate stationary distribution similar to the original proposal, along with some refinements in the estimates obtained using that distribution. |