We prove that throughout the satisfiable phase, the logarithm of the number of satisfying assignments of a random 2-SAT formula satisfies a central limit theorem. This implies that the log of the number of satisfying assignments exhibits fluctuations of order $\sqrt n$, with $n$ the number of variables. The formula for the variance can be evaluated effectively. By contrast, for numerous other random constraint satisfaction problems the typical fluctuations of the logarithm of the number of solutions are {\em bounded} throughout all or most of the satisfiable regime.

翻译：我们证明，在整个可满足阶段，随机2-SAT公式的满足赋值数量的对数满足中心极限定理。这表明满足赋值数量的对数呈现$\sqrt n$量级的波动，其中$n$为变量数。该方差公式可被有效计算。相比之下，对于许多其他随机约束满足问题，在可满足区域的全部或大部分范围内，解的数量对数的典型波动是{\em有界的}。