  The renormalization group equations for large-scale structure (RG-LSS)
describe how the bias and stochastic (noise) parameters -- both of matter and
biased tracers such as galaxies -- evolve as a function of the cutoff $\Lambda$
of the effective field theory. In previous work, we derived the RG-LSS
equations for the bias parameters using the Wilson-Polchinski framework. Here,
we extend these results to include stochastic contributions, corresponding to
terms in the effective action that are higher order in the current $J$. We show
that the RG equations exhibit an interesting, previously unnoticed structure at
all orders in $J$, which implies that a single nonlinear bias term immediately
generates all stochastic moments through RG evolution. We then derive the
nonlinear RG evolution of the (leading-derivative) stochastic parameters for
all $n$-point functions, and show that this evolution is controlled by a
different, lower scale than the nonlinear scale. This has implications for the
optimal choice of the renormalization scale when comparing the theory with data
to obtain cosmological constraints.
