  We present some estimates for the memory kernel function in the generalized
Langevin equation, derived using the Mori-Zwanzig formalism from a
one-dimensional lattice model, in which the particles interactions are through
nearest and second nearest neighbors. The kernel function can be explicitly
expressed in a matrix form. The analysis focuses on the decay properties, both
spatially and temporally, revealing a power-law behavior in both cases. The
dependence on the level of coarse-graining is also studied.
