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

In this manuscript we analyse the behaviour of the probability densityfunction of the sum of $N$ deterministic variables generated from the trianglemap of Casati-Prosen. For the case in which the map is both ergodic and mixingthe resulting probability density function quickly concurs with the Normaldistribution. When these properties are modified the resulting probabilitydensity functions are described by power-laws. Moreover, contrarily to what itwould be expected, as the number of added variables $N$ increases the distanceto Gaussian distribution increases. This behaviour goes against standardcentral limit theorem. By extrapolation of our finite size results we previewthat in the limit of $N$ going to infinity the distribution has the sameasymptotic decay as a Lorenztian (or a $q=2$-Gaussian).

On the role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables