Large Deviations for a Point Process of Bounded Variability

#### S. Goldstein, J.L. Lebowitz, E.R. Speer

2006, v.12, Issue 2, 235-256

ABSTRACT

We consider a one-dimensional translation invariant point process of density one with uniformly bounded variance of the number $N_I$ of particles in any interval $I$. Despite this suppression of fluctuations we obtain a large deviation principle with rate function $\cal F(\rho)\simeq-L^{-1}\log\Prob(\rho)$ for observing a macroscopic density profile $\rho(x)$, $x\in[0,1]$, corresponding to the coarse-grained and rescaled density of the points of the original process in an interval of length $L$ in the limit $L\to\infty$. $\cal F(\rho)$ is not convex and is discontinuous at $\rho\equiv1$, the typical profile.

Keywords: large deviations,hyperuniform point processes,controlled variability