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$\\lambda$ on the behavior of the system, \\begin{align*}\n  \\rm{d} u_t(x) = & (\\mathcal{G}u_t)(x)\\,\\rm{d} t + \\lambda\\sigma(u_t(x))\\rm{d} B_t(x)\n  \\qquad[t>0,\\ x\\in\\mathbf{Z}^d],\n  &u_0(x)=c_0\\delta_0(x). \\end{align*}\n  We show that for any $\\lambda>0$ in dimensions one and two the total mass 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