arXiv subjects

Markus Flury

Publications and source records attributed to Markus Flury.

2 recordsLinked to original sources

arXiv2008

Coincidence of Lyapunov exponents for random walks in weak random potentials

We investigate the free energy of nearest-neighbor random walks on $\mathbb{Z}^d$, endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions $d\geq4$, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.

math.PR↗

arXiv2006

Large Deviations and Phase Transition for Random Walks in Random Nonnegative Potentials

We establish large deviation principles and phase transition results for both quenched and annealed settings of nearest-neighbor random walks with constant drift in random nonnegative potentials on $\mathbb Z^d$. We complement the analysis of \cite{Zer}, where a shape theorem on the Lyapunov functions and a large deviation principle in absence of the drift are achieved for the quenched setting.

math.PR↗