Abstract

We consider a one-dimensional translation invariant point process of density one with uniformly bounded variance of the number NI of particles in any interval I. Despite this suppression of fluctuations we obtain a large deviation principle with rate function F(ρ) −L−1 log Prob(ρ) for observing a macroscopic density profile ρ(x), x ∈ [0, 1], corresponding to the coarse-grained and rescaled density of the points of the original process in an interval of length L in the limit L → ∞. F(ρ) is not convex and is discontinuous at ρ ≡ 1, the typical profile.