  We use a combination of analytical and numerical methods to study out-of-time
order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find
that at a given order of N , the standard result for the q-local, all-to-all
SYK, obtained through the sum over ladder diagrams, is corrected by a series in
the sparsity parameter, k. We present an algorithm to sum the diagrams at any
given order of 1/(kq)n. We also study OTOCs numerically as a function of the
sparsity parameter and determine the Lyapunov exponent. We find that numerical
stability when extracting the Lyapunov exponent requires averaging over a
massive number of realizations. This trade-off between the efficiency of the
sparse model and consistent behavior at finite N becomes more significant for
larger values of N .
