We study the transport properties of a quasi-two-dimensional diffusive normalmetal film attached to a superconductor. We demonstrate that the properties ofsuch films can essentially differ from those of quasi-one-dimensional systems:in the presence of the proximity induced superconductivity in a sufficientlywide film its conductance may not only increase but also decrease withtemperature. We develop a quantitative theory and discuss the physical natureof this effect. Our theory provides a natural explanation for recentexperimental findings referred to as the ``anomalous proximity effect''.
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