An Upper Bound of the Mean Growth in the Williams – Bjerknes Tumour Model

@inproceedings{Martnez2005AnUB,
  title={An Upper Bound of the Mean Growth in the Williams – Bjerknes Tumour Model},
  author={Francisco Mart{\'i}nez and A. R. VILLENA},
  year={2005}
}
We consider a cancer started with a single cancerous cell which spreads through an epithelial basal layer according to the Williams– Bjerknes tumour model on the lattice Z2. We prove that the expected number μ(t) of cancerous cells at time t satisfies lim t→+∞ μ(t) tρ = 0 for all ρ > 2.