  We consider the Eden model on the d-dimensional hypercubical unoriented
lattice , for large d. Initially, every lattice point is healthy, except the
origin which is infected. Then, each infected lattice point contaminates any of
its neighbours with rate 1. The Eden model is equivalent to first passage
percolation, with exponential passage times on edges. The Eden conjecture
states that the limit shape of the Eden model is a Euclidean ball. By putting
the computations of Dhar [Dha88] a little further with modern computers and
efficient implementation we obtain improved bounds for the speed of infection.
This shows that the Eden conjecture does not hold in dimension superior to 22
(the lower known dimension was 35).

Probability