  We calculate the redshift space correlation function and the power spectrum
of density peaks of a Gaussian random field. In the linear regime k < 0.1
h/Mpc, the redshift space power spectrum is
  P^s_{pk}(k,u) = exp(-f^2 s_{vel}^2 k^2 u^2) * [b_{pk}(k) + b_{vel}(k) f
u^2]^2 * P_m(k), where u is the angle with respect to the line of sight,
s_{vel} is the one-dimensional velocity dispersion, f is the growth rate, and
b_{pk}(k) and b_{vel}(k) are k-dependent linear spatial and velocity bias
factors. For peaks, the value of s_{vel} depends upon the functional form of
b_{vel}. The peaks model is remarkable because it has unbiased velocities --
peak motions are driven by dark matter flows -- but, in order to achieve this,
b_{vel} is k-dependent. We speculate that this is true in general: k-dependence
of the spatial bias will lead to k-dependence of b_{vel} even if the biased
tracers flow with the dark matter. Because of the k-dependence of the linear
bias parameters, standard manipulations applied to the peak model will lead to
k-dependent estimates of the growth factor that could erroneously be
interpreted as a signature of modified dark energy or gravity. We use the
Fisher formalism to show that the constraint on the growth rate f is degraded
by a factor of two if one allows for a k-dependent velocity bias of the peak
type. We discuss a simple estimate of nonlinear evolution and illustrate the
effect of the peak bias on the redshift space multipoles. For k < 0.1 h/Mpc,
the peak bias is deterministic but k-dependent, so the configuration space bias
is stochastic and scale dependent, both in real and redshift space. We provide
expressions for this stochasticity and its evolution (abridged).
