  The two main features of the Aharonov-Bohm effect are the topological
dependence of accumulated phase on the winding number around the magnetic
fluxon, and non-locality -- local observations at any intermediate point along
the trajectories are not affected by the fluxon. The latter property is usually
regarded as exclusive to quantum mechanics. Here we show that both the
topological and non-local features of the Aharonov-Bohm effect can be
manifested in a classical model that incorporates random noise. The model also
suggests new types of multi-particle topological non-local effects which have
no quantum analog.
