  Recent experiments on atomic-scale metallic contacts have shown that the
quantization of the conductance appears clearly only after the average of the
experimental results. Motivated by these results we have analyzed a simplified
model system in which a narrow neck is randomly coupled to wide ideal leads,
both in absence and presence of time reversal invariance. Based on Random
Matrix Theory we study analytically the probability distribution for the
conductance of such system. As the width of the leads increases the
distribution for the conductance becomes sharply peaked close to an integer
multiple of the quantum of conductance. Our results suggest a possible
statistical origin of conductance quantization in atomic-scale metallic
contacts.
