Abstract
Williams and Bjerknes introduced in 1972 a stochastic model for the spread of cancer cells; independently, this model has since surfaced within the field of interacting particle systems as the biased voter model. Cells, normal and abnormal (cancerous), are situated on a planar lattice. With each cellular division, one daughter stays put, while the other usurps the position of a neighbor; abnormal cells reproduce at a faster rate than normal cells. We treat here the long-term behavior of this system. In particular, we show that, provided it lives forever, the tumour will eventually contain a ball of linearly expanding radius. This also demonstrates the ergodicity of the interacting particle system, the coalescing random walk with nearest neighbor births. Our techniques include the use of dual processes, and of different numerical computations involving the use of imbedded processes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
