  We present a numerical study of lasing modes in diffusive random media with
local pumping. The reabsorption of emitted light suppresses the feedback from
the unpumped part of the sample and effectively reduces the system size. The
lasing modes are dramatically different from the quasimodes of the passive
system (without gain or absorption). Even if all the quasimodes of a passive
diffusive system are extended across the entire sample, the lasing modes are
still confined in the pumped volume with an exponential tail outside it. The
reduction of effective system volume by absorption broadens the distribution of
decay rates of quasimodes and facilitates the occurrence of discrete lasing
peaks.
