Non-Stationary Chaos Revisited from Large Deviation Theory

Large-deviation approach to space-time chaos.

In this Letter, we show that the analysis of Lyapunov-exponent fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a gaussian approximation for the large-deviation function that quantifies the fluctuation probability. More precisely, a diffusion matrix D (a dynamical invariant itself) is measured and analyzed in terms of its principal ...

Large Deviation Theory

If we draw a random variable n times from Q, the probability distribution of the sum of the random variables is given by Q. This is the convolution of Q with itself n times. As n → ∞, Q tends to a normal distribution by the central limit theorem. This is shown in Figure 1. The top line is a computed normal distribution with the same mean as Q. However, as shown in Figure 3, when plotted on a lo...

Large deviation theory and applications

Large deviation theory deals with the decay of the probability of increasingly unlikely events. It is one of the key techniques of modern probability, a role which is emphasised by the recent award of the Abel prize to S.R.S. Varadhan, one of the pioneers of the subject. The subject is intimately related to combinatorial theory and the calculus of variations. Applications of large deviation the...

A large-deviation approach to space-time chaos

Pavel V. Kuptsov ∗ and Antonio Politi 3 Department of Technical Cybernetics and Informatics, Saratov State Technical University, Politekhnicheskaya 77, Saratov 410054, Russia CNR Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom (Dated: ...

Large deviation principle in logarithmic potential theory