## Large Deviations for a Point Process of Bounded Variability

### Authors: S. Goldstein, J. L. Lebowitz and E. R. Speer

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 $\F(\rho)\simeq-L^{-1}\log\Prob(\rho)$ 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 $L\to\infty$. $\F(\rho)$ is not convex and is discontinuous at $\rho\equiv1$, the typical profile.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2006/2006-07.ps.gz