# Topology and local geometry of the Eden model

@article{Manin2020TopologyAL, title={Topology and local geometry of the Eden model}, author={Fedor Manin and {\'E}rika Rold{\'a}n and Benjamin Schweinhart}, journal={arXiv: Probability}, year={2020} }

The Eden cell growth model is a simple discrete stochastic process which produces a "blob" in $\mathbb{R}^d$: start with one cube in the regular grid, and at each time step add a neighboring cube uniformly at random. This process has been used as a model for the growth of aggregations, tumors, and bacterial colonies and the healing of wounds, among other natural processes. Here, we study the topology and local geometry of the resulting structure, establishing asymptotic bounds for Betti numbers… Expand

#### Figures and Tables from this paper

#### References

SHOWING 1-10 OF 49 REFERENCES

Similarity of ensembles of trajectories of reversible and irreversible growth processes.

- Physics, Chemistry
- Physical review. E
- 2017

Volume Optimal Cycle: Tightest representative cycle of a generator on persistent homology

- Mathematics, Computer Science
- SIAM J. Appl. Algebra Geom.
- 2018