  We study a general class of discrete $p$-Laplace operators in the random
conductance model with long-range jumps and ergodic weights. Using a
variational formulation of the problem, we show that under the assumption of
bounded first moments and a suitable lower moment condition on the weights, the
homogenized limit operator is a fractional $p$-Laplace operator.
  Under strengthened lower moment conditions, we can apply our insights also to
the spectral homogenization of the discrete Laplace operator to the continuous
fractional Laplace operator.
