Correlation of Occupation Profiles in Invasion Percolation

We study theoretically and by simulation the spatial correlation of the fluctuations of the transversely averaged fraction of the invading phase in [ital invasion] [ital percolation]. For an uncorrelated lattice, the profile has the correlation structure of the trace of [ital fractional] [ital Brownian] [ital motion] (FBM) with [ital Hurst] exponent [ital H]=[ital D][minus]2 for 3D percolation and [ital H]=[ital D][minus]1.5 for 2D percolation, where [ital D] is the fractal dimension of the percolation cluster. Extension to correlated percolation shows similar results, with the FBM signal displaying [ital persistent] correlations ([ital H][gt]0.5) in 3D and [ital antipersistent] correlations ([ital H][lt]0.5) in 2D percolation. Experiments of nonwetting fluid invasion in porous media confirm the theory in 3D.