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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We compute the exact asymptotics for the cumulants of linear statisticsassociated with the zeros counting measure of a large class of real Gaussianprocesses. Precisely, we show that if the underlying covariance function isregular and square integrable, the cumulants of order higher than two of thesestatistics asymptotically vanish. This result implies in particular that thenumber of zeros of such processes satisfies a central limit theorem. Ourmethods refines the recent approach by T. Letendre and M. Ancona and allows usto prove a stronger quantitative asymptotics, under weaker hypotheses on theunderlying process. The proof exploits in particular the elegant interplaybetween the combinatorial structures of cumulants and factorial moments inorder to simplify the determination of the asymptotics of nodal observables.The class of processes addressed by our main theorem englobes as motivatingexamples random Gaussian trigonometric polynomials, random orthogonalpolynomials and the universal Gaussian process with sinc kernel on the realline, for which the asymptotics of higher moments of the number of zeros wereso far only conjectured.

Cumulants asymptotics for the zeros counting measure of real Gaussian processes