  We investigate the distribution of energy density in a stationary
self-reproducing inflationary universe. We show that the main fraction of
volume of the universe in a state with a given density $\rho$ at any given
moment of time $t$ in synchronous coordinates is concentrated near the centers
of deep exponentially wide spherically symmetric holes in the density
distribution. A possible interpretation of this result is that a typical
observer should see himself living in the center of the world. Validity of this
interpretation depends on the choice of measure in quantum cosmology. Our
investigation suggests that unexpected (from the point of view of inflation)
observational data, such as possible local deviations from $\Omega = 1$, or
possible dependence of the Hubble constant on the length scale, may tell us
something important about quantum cosmology and particle physics at nearly
Planckian densities.
