Positive invariant fields of the nonlinear multiplicative stochastic heat equation in weak disorder are in one-to-one correspondence with bounded positive harmonic functions, inheriting the Martin boundary structure.
Fluctuations of a nonlinear stochastic heat equation in dimensions three and higher
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Martin Boundary and the Nonlinear Multiplicative Stochastic Heat Equation in Weak Disorder
Positive invariant fields of the nonlinear multiplicative stochastic heat equation in weak disorder are in one-to-one correspondence with bounded positive harmonic functions, inheriting the Martin boundary structure.