Anomalous scaling of dynamical large deviations of stationary Gaussian processes

TL;DR

This paper investigates the large deviation behavior of long-time averages of stationary Gaussian processes, revealing anomalous scaling phenomena that extend beyond specific cases like the Ornstein-Uhlenbeck process.

Contribution

It demonstrates that the anomalous scaling of large deviations, previously observed in specific processes, applies broadly to a class of correlated, non-Markovian stationary Gaussian processes.

Findings

Anomalous scaling observed for long-time averages.

Scaling behavior extends beyond Ornstein-Uhlenbeck process.

Applicable to a broad class of Gaussian processes.

Abstract

Employing the optimal fluctuation method (OFM), we study the large deviation function of long-time averages $(1/T)\int_{-T/2}^{T/2} x^n(t) dt$, $n=1,2, \dots$, of centered stationary Gaussian processes. These processes are correlated and, in general, non-Markovian. We show that the anomalous scaling with time of the large-deviation function, recently observed for $n>2$ for the particular case of the Ornstein-Uhlenbeck process, holds for a whole class of stationary Gaussian processes.