On nonlinear diffusion with multiplicative noise

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Abstract
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a "wall" limiting the motion of the diffusing field. A dynamic phase transition occurs when the system "unbinds" from the wall. Two different universality classes, corresponding to the cases of an "upper" and a "lower" wall, are identified and their critical properties are characterized. While the lower wall problem can be understood by applying the knowledge of linear diffusion with multiplicative noise, the upper wall problem exhibits an anomaly due to an effective long-ranged repulsion exerted by the wall.
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