  We study the distribution of neighborhoods across a set of 12 global cities
and find that the distribution of neighborhood sizes follows exponential decay
across all cities under consideration. We are able to analytically show that
this exponential distribution of neighbourhood sizes is consistent with the
observed Zipf's Law for city sizes. We attempt to explain the emergence of
exponential decay in neighbourhood size using a model of neighborhood dynamics
where migration into and movement within the city are mediated by wealth. We
find that, as observed empirically, the model generates exponential decay in
neighborhood size distributions for a range of parameter specifications. The
use of a comparative wealth-based metric to assess the relative attractiveness
of a neighborhood combined with a stringent affordability threshold in
mediating movement within the city are found to be necessary conditions for the
the emergence of the exponential distribution. While an analytical treatment is
difficult due to the globally coupled dynamics, we use a simple
two-neighbourhood system to illustrate the precise dynamics yielding
equilibrium non-equal neighborhood size distributions.
