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The asymptotic behaviour of an invasion process

Published online by Cambridge University Press:  14 July 2016

F. P. Kelly
F. P. Kelly*
Affiliation:
University of Cambridge
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Abstract

Black and white cells are positioned at the vertices of a rectangular lattice. When a cell division occurs, the daughter cells are of the same colour as the parent cell; one of them replaces an adjacent cell and the other remains in the position of the parent cell. In one variant of the model it is assumed that whenever a white cell appears at the origin it is transformed into a black cell; apart from this the black and white cells are equally competitive and in particular they divide at the same rate. Initially, only the cell at the origin is black. The asymptotic behaviour of the black clone is investigated.

Keywords

SPATIAL PROCESSINVASIONTUMOUR GROWTHRANDOM WALK

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 14 , Issue 3 , September 1977 , pp. 584 - 590
Copyright
Copyright © Applied Probability Trust 1977 

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