numerical check as well), that the coefficient functions $Z_0(m,L)$ and $Z_1(m,L)$ remain finite in this case, and the contribution of $Z_0(m,L)$ is negligible in comparison with $m Z_1(m,L)$ in . One can use Eqs.  and  in order to estimate  in the leading approximation: $$\frac{2^{4L}}{\pi L}\,e^{-m^2/2L}(M+2mZ_1(m,L)-
(\pi L)^{1/2}e^{m^2/4L}).
\label{53}$$ Because of the behavior of the coefficient $Z_1(m,L)$, the corresponding contribution in  may turn out to be comparable with $M$. The relation  demonstrates that the description of the random walks considered in the representation of the superposition of the eigen-states is more complicated than the one in the ferromagnetic case. This description can be regarded as a simultaneous walks of the initial (i.e., principal) and virtual pedestrians. The ending points of the trajectories belonging to all the three segments of the dashed broken line on the figure (see the representation of two-dimensional random walks ) correspond to comparable contributions into the estimate . In certain cases, characterized by the limiting behavior of the ratio $m^2/L$, the contribution of the segment between the points $(m,0)$ and $(0,m)$ can become dominating.

Conclusion {#sec4}
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It is shown that the correlation functions of the $XX$ Heisenberg magnet, calculated over the superposition of the eigen-states, as 