You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We consider the solution @math to the one-dimensional parabolic Anderson model with homogeneous initial condition @math , 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 @math -th annealed Lyapunov exponents for all @math These results enable us to prove the heuristically plausible fact that the @math -th annealed Lyapunov exponent converges to the quenched Lyapunov exponent as @math Furthermore, we show that @math is @math -intermittent for @math large enough. As a byproduct, we compute the optimal quenched speed of the random walk appearing in the Feynman-Kac representation of @math 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.

Cited Abstract(s):
[1]: Let (η n ) be the infinite particle system on ℤ whose evolution is as follows. At each unit of time each particle independently is replaced by a new generation. The size of a new generation descending from a particle at sitex has distributionF x and each of its members independently jumps to sitex±1 with probability (1±h) 2,h∈[0, 1]. The sequence F x is i.i.d. with uniformly bounded second moment and is kept fixed during the evolution. The initial configurationη0 is shift invariant and ergodic.
A situation similar in spirit to ours has been examined in the seminal article [1] by Greven and den Hollander, motivated from the point of view of population dynamics. The model treated there is a discrete-time branching model in random environment with drift and corresponds to the case of a bounded i.i.d. potential. In particular, their motivation stems from the discrete-time analogue described at the end of section . The results are formulated by the use of nontrivial variational formulae. While the authors concentrate on the explicit dependence of the results on the drift parameter @math an advantage of our approach is that we may compute the @math -th annealed Lyapunov exponents for all @math and characterise them in a simpler way.