  We study the random fluctuations of the transmission in disordered
quasi-one-dimensional systems such as disordered waveguides and/or quantum
wires whose random configurations of disorder are characterized by density
distributions with a long tail known as L\'evy distributions. The presence of
L\'evy disorder leads to large fluctuations of the transmission and anomalous
localization, in relation to the standard exponential localization (Anderson
localization). We calculate the complete distribution of the transmission
fluctuations for different number of transmission channels in the presence and
absence of time-reversal symmetry. Significant differences in the transmission
statistics between disordered systems with Anderson and anomalous localizations
are revealed. The theoretical predictions are independently confirmed by tight
binding numerical simulations.
