avoids completely analyzing the actual distribution of $x^{(t)}$, he does show the following property of this distribution which in turn allows him to use an average drift approach. In this way, he omits the need for point-wise drift. Jägersküpper’s simple observation is that at any time step $t$, the more valuable bits are more likely to be in the right setting (cf. Theorem 1 in [@Jagerskupper08]).

\[thm:jagerskupper\] Let $n\in\mathbb{N}$ be a positive integer and let $x^{(t)}$ denote the random individual (distributed over $\{0,1\}^n$) after $t\in\mathbb{N}$ iterations of the (1+1) EA minimizing a linear function $f\colon\{0,1\}^n\to\mathbb{R}$. Then $${\ensuremath{\mathrm{Pr}}}[x^{(t)}_1 = 0]\le\dots\le{\ensuremath{\mathrm{Pr}}}[x^{(t)}_n = 0].$$ Moreover, for all $k\in\{0,\dots,n\}$, this statement remains true if we condition on ${\textsc{OneMax}\xspace}(x)=k$.

Using this theorem, he was able to show a lower bound of ${\Omega(1/n)}$ for the drift of [<span style="font-variant:small-caps;">OneMax</span>]{}as potential function for any linear function.

\[lem:drift\] Let $n\in\mathbb{N}$ be a positive integer and let $f\colon\{0,1\}^n\to\mathbb{N}$ be a linear function. Let $x^{(t)}$ be the individual in the $t$-th iteration of the (1+1) EA minimizing $f$. Then $${\ensuremath{\operatorname{E}}}[{\textsc{OneMax}\xspace}(x^{(t)})-{\textsc{OneMax}\xspace}(x^{(t+1)})\mid {\textsc{OneMax}\xspace}(x^{(t)})=k]\ge\frac{({\mathrm{e}\xspace}-2)k}{{\mathrm{e}\xspace}n}.$$ holds for all $k\in\{0,\dots,n\}$ and $t\in\mathbb{N}$.

In addition to a more natural proof of the $O(n \ln(n))$ bound for expected optimization time of the (1+1) EA minimizing a linear 