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The amount $Q$ of particles that are transported via a path of motion ischaracterized by its expectation value $<Q>$ and by its variance $Var(Q)$. Weanalyze what happens if a particle has two optional paths available to get fromone site to another site, and in particular what is $Var(Q)$ for the currentwhich is induced in a quantum stirring device. It turns out that coherentsplitting and the stirring effect are intimately related and cannot beunderstood within the framework of the prevailing probabilistic theory.

Counting statistics in multiple path geometries and the fluctuations of the integrated current in a quantum stirring device