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

In this paper we will prove a shape theorem for the last passage percolationmodel on a two dimensional $F$-compound Poisson process, called the Hammersleymodel with random weights. We will also provide diffusive upper bounds forshape fluctuations. Finally we will indicate how these results can be used toprove existence and coalescence of semi-infinite geodesics in some fixeddirection $\alpha$, following an approach developed by Newman and co-authors,and applied to the classical Hammersley process by W\"uthrich. These resultswill be crucial in the development of an upcoming paper on the relation betweenBusemann functions and equilibrium measures in last passage percolation models.

A shape theorem and semi-infinite geodesics for the Hammersley model with random weights