Abstract
Roughness of random walks in the presence of a Laplacian field is studied in two dimensions for various strengths of the field parametrized by η. We find an ηc∼4.5±0.3 at which a transition occurs from a tortuous fractal structure to a one-dimensional profile of the walk. At ηc, the walks are self-affine with a roughness exponent ζ=0.80±0.05. For increasing η-values, the roughness exponent increases.