Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters

Understand

We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IIC's).

• First we compute the exact decay rate of the distribution of both the weight of the kth outlet and the volume of the kth pond.
• Next we prove bounds for all moments of the distribution of the number of outlets in an annulus.
• This result leads to almost sure bounds for the number of outlets in a box B(2^n) and for the decay rate of the weight of the kth outlet to p_c.