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Convergence Towards an Asymptotic Shape in First-Passage Percolation on Cone-Like Subgraphs of the Integer Lattice

Daniel Ahlberg (Institutionen för matematiska vetenskaper, matematisk statistik)
Journal of Theoretical Probability (0894-9840). Vol. 28 (2015), 1, p. 198-222.
[Artikel, refereegranskad vetenskaplig]

In first-passage percolation on the integer lattice, the shape theorem provides precise conditions for convergence of the set of sites reachable within a given time from the origin, once rescaled, to a compact and convex limiting shape. Here, we address convergence towards an asymptotic shape for cone-like subgraphs of the lattice, where . In particular, we identify the asymptotic shapes associated with these graphs as restrictions of the asymptotic shape of the lattice. Apart from providing necessary and sufficient conditions for - and almost sure convergence towards this shape, we investigate also stronger notions such as complete convergence and stability with respect to a dynamically evolving environment.

Nyckelord: First-passage percolation, Shape theorem, Large deviations, Dynamical stability



Denna post skapades 2015-04-22. Senast ändrad 2015-04-22.
CPL Pubid: 215550

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Sannolikhetsteori och statistik

Chalmers infrastruktur