Large deviations for noninteracting infinite particle systems
Let \(X=\{x_ i\}\) stand for a point configuration, \(w=\{w_ i(s)\}\) for the trajectory of a configuration, and \(P_{a,b}\) \((P_ X\), resp.) denote the probability distribution of the particle system with initial distribution \(\mu_{a,b}=\mu_{a+b \exp (x)}\quad (\delta_ X,\quad resp.).\) The author considers Brownian motion with constant drift and proves large deviation rates for the empirical density \[ D_{t,w}(K)=t^{-1}\int^{1}_{0}\sum_{i}I_ K(w_ i(s))ds\quad (K\subset R,\quad measurable) \] under \(P_{a,b}\) (Section 1) as well as under \(P_ X\) (Section 2). Initially a lower bound is found for the rate function, then a cumulant generating function estimation yields an upper bound, and finally the equivalence of upper and lower bounds is shown. At the end of the paper the author contrasts his model to that in the paper of \textit{M. D. Donsker} and \textit{S. R. S. Varadhan}, J. Stat. Phys. 46, 1195-1232 (1987), bearing the same title.
scientific article; zbMATH DE number 4080520