  The evolution of the cluster mass function and the cluster correlation
function from z = 0 to z = 3 are determined using 10^6 clusters obtained from
high-resolution simulations of the current best-fit LCDM cosmology (\Omega_m =
0.27, \sigma_8 = 0.84, h = 0.7). The results provide predictions for
comparisons with future observations of high redshift clusters. A comparison of
the predicted mass function of low redshift clusters with observations from
early Sloan Digital Sky Survey data, and the predicted abundance of massive
distant clusters with observational results, favor a slightly larger amplitude
of mass fluctuations (\sigma_8 = 0.9) and lower density parameter (\Omega_m =
0.2); these values are consistent within 1-\sigma with the current
observational and model uncertainties. The cluster correlation function
strength increases with redshift for a given mass limit; the clusters were more
strongly correlated in the past, due to their increasing bias with redshift -
the bias reaches b = 100 at z = 2 for M > 5 x 10^13 h^-1 M_sun. The
richness-dependent cluster correlation function, represented by the correlation
scale versus cluster mean separation relation, R0-d, is generally consistent
with observations. This relation can be approximated as R_0 = 1.7 d^0.6 h^-1
Mpc for d = 20 - 60 h^-1 Mpc. The R0-d relation exhibits surprisingly little
evolution with redshift for z < 2; this can provide a new test of the current
LCDM model when compared with future observations of high redshift clusters.
