uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
First Passage Percolation on \(\mathbb {Z}^2\): A Simulation Study
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden..
2015 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 161, no 3, 657-678 p.Article in journal (Refereed) Published
Abstract [en]

First passage percolation on is a model for describing the spread of an infection on the sites of the square lattice. The infection is spread via nearest neighbor sites and the time dynamic is specified by random passage times attached to the edges. In this paper, the speed of the growth and the shape of the infected set is studied by aid of large-scale computer simulations, with focus on continuous passage time distributions. It is found that the most important quantity for determining the value of the time constant, which indicates the inverse asymptotic speed of the growth, is , where are i.i.d. passage time variables. The relation is linear for a large class of passage time distributions. Furthermore, the directional time constants are seen to be increasing when moving from the axis towards the diagonal, so that the limiting shape is contained in a circle with radius defined by the speed along the axes. The shape comes closer to the circle for distributions with larger variability.

Place, publisher, year, edition, pages
2015. Vol. 161, no 3, 657-678 p.
Keyword [en]
First passage percolation, Growth model, Time constant, Asymptotic shape, Computer simulation
National Category
Probability Theory and Statistics
URN: urn:nbn:se:uu:diva-266689DOI: 10.1007/s10955-015-1356-0ISI: 000362738300007OAI: oai:DiVA.org:uu-266689DiVA: diva2:868915
Available from: 2015-11-12 Created: 2015-11-10 Last updated: 2016-02-17Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Alm, Sven Erick
By organisation
Analysis and Probability Theory
In the same journal
Journal of statistical physics
Probability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 373 hits
ReferencesLink to record
Permanent link

Direct link