English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

It is well known that every stochastic flow on Rd, whose one-point motion has an invariant measure m, gives rise to a measure-valued process (v t, t≥0) with v 0=m, which converges almost surely to a random measure ℝd, called the statistical equilibrium. We prove here that if the flow is spatially homogeneous and isotropic, and if either the covariance is smooth and the top Lyapounov exponent is strictly negative, or if the flow is “of coalescing type” (these phenomena can only occur when d≤3), then v ∞=0 a.s.

The statistical equilibrium of an isotropic stochastic flow with negative lyapounov exponents is trivial