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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove a multidimensional ergodic theorem with weighted averages for theaction of the group $\mathbb{Z}^d$ on a probability space. At level $n$ weightsare of the form $n^{-d} \psi(j/n)$, $ j\in \mathbb{Z}^d$, for real functions$\psi$ decaying suitably fast. We discuss applications to random measures andto quenched stochastic homogenization of random walks (RWs) on simple pointprocesses with long-range random jump rates, allowing to remove the technicalAssumption (A9) from \cite[Theorem~4.4]{Fhom1}. This last result concerns alsosome semigroup and resolvent convergence particularly relevant for thederivation of the quenched hydrodynamic limit of interacting particle systems(IPSs) via homogenization and duality. As a consequence we show that also thequenched hydrodynamic limit of the symmetric simple exclusion process on pointprocesses stated in \cite[Theorem~4.1]{F_SEP} remains valid when removing theabove mentioned Assumption (A9).

An ergodic theorem with weights and applications to random measures, RW homogenization and IPS hydrodynamics on point processes