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

A small world is obtained from the $d$-dimensional torus of size 2L addingrandomly chosen connections between sites, in a way such that each site hasexactly one random neighbour in addition to its deterministic neighbours. Westudy the asymptotic behaviour of the meeting time $T_L$ of two random walksmoving on this small world and compare it with the result on the torus. On thetorus, in order to have convergence, we have to rescale $T_L$ by a factor$C_1L^2$ if $d=1$, by $C_2L^2\log L$ if $d=2$ and $C_dL^d$ if $d\ge3$. We provethat on the small world the rescaling factor is $C^\prime_dL^d$ and identifythe constant $C^\prime_d$, proving that the walks always meet faster on thesmall world than on the torus if $d\le2$, while if $d\ge3$ this depends on theprobability of moving along the random connection. As an application, we obtainresults on the hitting time to the origin of a single walk and on theconvergence of coalescing random walk systems on the small world.

The small world effect on the coalescing time of random walks