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- W2950668458 abstract "We consider the solution $u$ to the one-dimensional parabolic Anderson model with homogeneous initial condition $u(0, cdot) equiv 1$, arbitrary drift and a time-independent potential bounded from above. Under ergodicity and independence conditions we derive representations for both the quenched Lyapunov exponent and, more importantly, the $p$-th annealed Lyapunov exponents for {it all} $p in (0, infty).$ These results enable us to prove the heuristically plausible fact that the $p$-th annealed Lyapunov exponent converges to the quenched Lyapunov exponent as $p downarrow 0.$ Furthermore, we show that $u$ is $p$-intermittent for $p$ large enough. As a byproduct, we compute the optimal quenched speed of the random walk appearing in the Feynman-Kac representation of $u$ under the corresponding Gibbs measure. In this context, depending on the negativity of the potential, a phase transition from zero speed to positive speed appears." @default.
- W2950668458 created "2019-06-27" @default.
- W2950668458 creator A5035970780 @default.
- W2950668458 date "2008-03-10" @default.
- W2950668458 modified "2023-10-01" @default.
- W2950668458 title "Lyapunov exponents for the one-dimensional parabolic Anderson model with drift" @default.
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