Revision 1

Accepted · first revision · record

Title: When single optimal paths dominate extreme events
Plain: For very rare large events in noisy or chaotic systems, theory often assumes they occur along one most likely route, called an instanton. Whether and when that holds in high-dimensional systems like turbulence decides whether extremes can be computed rather than waited for.
Precise: For stochastically forced systems (Burgers, 2D and 3D Navier-Stokes with Gaussian forcing of strength $\epsilon$) and for deterministic chaotic systems, determine the observables $O$ and thresholds $z$ for which $P(O > z)$ is given asymptotically ($z \to \infty \text{ or } \epsilon \to 0$) by a single minimizer of the Freidlin-Wentzell action, including the prefactor, and characterize failures due to fluctuations around the instanton or several competing paths. An answer is a classification with verified prefactors.
Settled by: Comparison of instanton predictions, including prefactors, with rare-event sampling of tails over many orders of magnitude for a set of flows and observables.
Kind: well-posed
Answer type: classification
References: (empty)
Literature status: partially-resolved
Status note: Instanton predictions match velocity-gradient tails in Burgers turbulence and some 2D flows; extremes in 3D Navier-Stokes turbulence are not settled.
Posed since: (empty)