  We consider the role of static disorder in the spin sector of the one- and
two-channel Kondo models. The distribution functions of the disorder-induced
effective energy splitting between the two levels of the Kondo impurity are
derived to the lowest order in the concentration of static scatterers. It is
demonstrated that the distribution functions are strongly asymmetric, with the
typical splitting being parametrically smaller than the average rms value. We
employ the derived distribution function of splittings to study the temperature
dependence of the low-temperature conductance of a sample containing an
ensemble of two-channel Kondo impurities. The results are used to analyze the
consistency of the two-channel Kondo interpretation of the zero-bias anomalies
observed in Cu/(Si:N)/Cu nanoconstrictions.
