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 the critical spread-out contact process in Z^d with d\ge1, whoseinfection range is denoted by L\ge1. In this paper, we investigate the r-pointfunction \tau_{\vec t}^{(r)}(\vec x) for r\ge3, which is the probability that,for all i=1,...,r-1, the individual located at x_i\in Z^d is infected at timet_i by the individual at the origin o\in Z^d at time 0. Together with theresults of the 2-point function in [van der Hofstad and Sakai, Electron. J.Probab. 9 (2004), 710-769; arXiv:math/0402049], on which our proofs cruciallyrely, we prove that the r-point functions converge to the moment measures ofthe canonical measure of super-Brownian motion above the upper-criticaldimension 4. We also prove partial results for d\le4 in a local mean-fieldsetting.

Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: I. The higher-point functions