  Consider the infinite Atlas model: a semi-infinite collection of particles
driven by independent standard Brownian motions with zero drifts, except for
the bottom-ranked particle which receives unit drift. We derive a continuum
one-parameter family of product-of-exponentials stationary gap distributions,
with exponentially growing density at infinity. This result shows that there
are infinitely many stationary gap distributions for the Atlas model, and hence
resolves a conjecture of Pal and Pitman (2008) in the negative. This result is
further generalized for infinite systems of competing Brownian particles with
generic rank-based drifts.
