Georgia Institute of Technology College of Sciences

The main work of this thesis is to numerically estimate some conjectured arm exponents when there exist certain number of open paths and closed dual paths that extend to the boundary of a box of sidelength N centering at the origin in bond invasion percolation on a plane square lattice by Monte-Carlo simulations. The result turns out to be supportive for the conjectured value. The numerical estimate for the acceptance profile of invasion percolation at the critical point is also obtained. An efficient algorithm to simulate invasion percolation and to find disjoint paths on most regular 2-dimensional lattices are also discussed.