  The time needed for a particle to exit a confining domain through a small
window, called the narrow escape time (NET), is a limiting factor of various
processes, such as some biochemical reactions in cells. Obtaining an estimate
of the mean NET for a given geometric environment is therefore a requisite step
to quantify the reaction rate constant of such processes, which has raised a
growing interest in the last few years. In this Letter, we determine explicitly
the scaling dependence of the mean NET on both the volume of the confining
domain and the starting point to aperture distance. We show that this
analytical approach is applicable to a very wide range of stochastic processes,
including anomalous diffusion or diffusion in the presence of an external force
field, which cover situations of biological relevance.
