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

We consider a system of non-interacting Brownian particles on the line withsteplike initial condition and study the statistics of the occupation time onthe positive half-line. We demonstrate that this system exhibits long-lastingmemory effects of the initialization. Specifically, we calculate the mean andthe variance of the occupation time, demonstrating that the memory effects inthe variance are determined by a generalized compressibility (or Fano factor),associated with the initial condition. In the particular case of theuncorrelated uniform initial condition we conduct a detailed study of twoprobability distributions of the occupation time: annealed (averaged over allpossible initial configurations) and quenched (for a typical configuration). Weshow that at large times both the annealed and the quenched distributions admitlarge deviation form and we compute analytically the associated rate functions.We verify our analytical predictions via numerical simulations using ImportanceSampling Monte-Carlo strategy.

Occupation time of a system of Brownian particles on the line with steplike initial condition