# 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… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 39 REFERENCES

## Statistical Topology of Embedded Graphs

VIEW 1 EXCERPT

## History of a stochastic growth model

VIEW 1 EXCERPT

## The size of the boundary in first-passage percolation

VIEW 2 EXCERPTS

## Fractals, Scaling and Growth Far from Equilibrium

VIEW 1 EXCERPT

## A Two-dimensional Growth Process

VIEW 1 EXCERPT

## 50 years of first passage percolation

VIEW 2 EXCERPTS