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 examine, for $-1<q<1$, $q$-Gaussian processes, i.e. families of operators(non-commutative random variables) $X_t=a_t+a_t^*$ -- where the $a_t$ fulfillthe $q$-commutation relations $a_sa_t^*-qa_t^*a_s=c(s,t)\cdot \id$ for somecovariance function $c(\cdot,\cdot)$ -- equipped with the vacuum expectationstate. We show that there is a $q$-analogue of the Gaussian functor of secondquantization behind these processes and that this structure can be used totranslate questions on $q$-Gaussian processes into corresponding (and muchsimpler) questions in the underlying Hilbert space. In particular, we use thisidea to show that a large class of $q$-Gaussian processes possess anon-commutative kind of Markov property, which ensures that there existclassical versions of these non-commutative processes. This answers an oldquestion of Frisch and Bourret \cite{FB}.Comment: AMS-TeX 2.

q -Gaussian Processes: Non-commutative and Classical Aspects