  We relate the anomalous noise found experimentally in spin ice to the
subdiffusion of magnetic monopoles. Because monopoles are emergent particles,
they do not move in a structureless vacuum. Rather, the underlying spin
ensemble filters the thermal white noise, leading to non-trivial coevolution.
Thus, monopoles can be considered as random walkers under the effect of
stochastic forces only as long as those are not trivially white, but instead
subsume the evolution of the spin vacuum. Via this conceptualization, we
conjecture relations between the color of the noise and other observables, such
as relaxation time, monopole density, the dynamic exponent, and the order of
the annihilation reaction, which lead us to introduce spin ice specific
critical exponents in a neighborhood of the ice manifold.
