  Local time is the measure of how much time a random walk has visited a given
position. In multiple scattering media, where waves are diffuse, local time
measures the sensitivity of the waves to the local medium's properties. Local
variations of absorption, velocity and scattering between two measurements
yield variations in the wave field. These variations are proportionnal to the
local time of the volume where the change happened and the amplitude of
variation. The wave field variations are measured using correlations and can be
used as input in a inversion algorithm to produce variation maps. The present
article gives the expression of the local time in dimensions one, two and three
and an expression of its fluctuations, in order to perform such inversions and
estimate their accuracy.
