随机势趋于零时格林函数的李雅普诺夫指数
Lyapunov exponents of Green's functions for random potentials tending to zero
摘要：
我们考虑淬火和退火的李雅普诺夫指数的格林函数的$-Δ+γV$，其中的潜力$V(x), x\in\Z^d$，是i.i.d.非负随机变量，$γ>0$是标量。我们提出了一个概率证明，这两个李雅普诺夫指数规模像$c\sqrtγ$作为$γ$趋于0。在此，对于淬火和退火指数，常数$c$是相同的，并且是明确计算的。这改进了以前由Wei-Min Wang得到的结果。我们还考虑了其他方法，使电位为零，而不是将其乘以一个小数字。
英文摘要：
We consider quenched and annealed Lyapunov exponents for the Green's function of $-Δ+γV$, where the potentials $V(x), x\in\Z^d$, are i.i.d. nonnegative random variables and $γ>0$ is a scalar. We present a probabilistic proof that both Lyapunov exponents scale like $c\sqrtγ$ as $γ$ tends to 0. Here the constant $c$ is the same for the quenched as for the annealed exponent and is computed explicitly. This improves results obtained previously by Wei-Min Wang. We also consider other ways to send the potential to zero than multiplying it by a small number.
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