  The Luttinger liquid in which the concentration of electrons varies randomly
with coordinate is considered. We study the fluctuations of the tunnel
conductance, caused by the randomness in the concentration. If the
concentration changes slowly on the scale of the Fermi wavelength, its prime
role reduces to the scattering of the plasmon waves, propagating along the
system. As a result of such a scattering, plasmons get localized. We show that
the localization length, $l_{\omega}$, of a plasmon with frequency $\omega$ is
inverse proportional to the square of the interaction strength and changes with
frequency as $l_{\omega}\propto \omega^{-2}$. If the relative variation of the
concentration is small, the randomness--induced correction to the tunnel
conductance, $\delta G(V)$, where $V$ is the applied bias, can be expressed
through the spectral characteristics of the localized plasmons. The magnitude
of the correction, $(\overline{ \delta G^2})^{1/2}/ G$, increases with $V$ as
$\sqrt V$. The typical period of the fluctuations in $\delta G(V)$ is of the
order of $V$. At a fixed $V$, the correlator of $\delta G$ at different points
of the liquid falls off with distance as a power law and oscillates with the
period which is one half of the wavelength of a plasmon with frequency $\omega
= eV/\hbar$.
