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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider a field f \( \circ {T}_1^{i_1}\circ \dots \circ {T}_d^{i_d} \) , where T1, . . . , Td are completely commuting transformations in the sense of Gordin. If one of these transformations is ergodic, we give sufficient conditions in the spirit of Hannan under which the partial sum process indexed by quadrants converges in distribution to a Brownian sheet. The proof combines a martingale approximation approach with a recent CLT for martingale random fields due to Volný. We apply our results to completely commuting endomorphisms of the m-torus. In that case, the conditions can be expressed in terms of the L2-modulus of continuity of f.

A Functional CLT for Fields of Commuting Transformations Via Martingale Approximation