Coincidence of Lyapunov exponents for random walks in weak random potentials. (English) Zbl 1156.60076

This paper deals with random walks on a multidimensional lattice, endowed with a drift along the first axis. The author proved the coincidence of quenched and annealed Lyapunov exponents for the ballistic regime in higher dimensions in case of the potential is small enough and investigated an estimate of the speed of convergence for the free energy. The results were obtained by using mainly renewal techniques and arguments from Ornstein-Zernike theory.


60K37 Processes in random environments
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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