  We demonstrate that human electrophysiological recordings of the local field
potential (LFP) from intracranial electrodes, acquired from a variety of
cerebral regions, show a ubiquitous $1/f^2$ scaling within the power spectrum.
We develop a quantitative model that treats the generation of these fields in
an analogous way to that of electronic shot noise, and use this model to
specifically address the cause of this $1/f^2$ Brownian noise. The model gives
way to two analytically tractable solutions, both displaying Brownian noise: 1)
uncorrelated cells that display sharp initial activity, whose extracellular
fields slowly decay and 2) rapidly firing, temporally correlated cells that
generate UP-DOWN states.
