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

In a recent paper, we presented a new definition of influences in productspaces of continuous distributions, and showed that analogues of the mostfundamental results on discrete influences, such as the KKL theorem, hold forthe new definition in Gaussian space. In this paper we prove Gaussian analoguesof two of the central applications of influences: Talagrand's lower bound onthe correlation of increasing subsets of the discrete cube, and theBenjamini-Kalai-Schramm (BKS) noise sensitivity theorem. We then use theGaussian results to obtain analogues of Talagrand's bound for all discreteprobability spaces and to reestablish analogues of the BKS theorem for biasedtwo-point product spaces.

Geometric Influences II: Correlation Inequalities and Noise Sensitivity