The nonlinear transport properties of nanometer-scale junctions formed between an inert metallic tip and an Ag film covered by a thin Ag$_{2}$S layer are investigated. Suitably prepared samples exhibit memristive behavior with technologically optimal ON and OFF state resistances yielding to resistive switching on the nanosecond time scale. Utilizing point contact Andreev reflection spectroscopy we studied the nature of electron transport in the active volume of the memristive junctions showing that both the ON and OFF states correspond to truly nanometer scale, highly transparent metallic channels. Our results demonstrate the merits of Ag$_{2}$S nanojunctions as nanometer-scale memory cells with GHz operation frequencies.
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