  Estimating numerically the spectral radius of a random walk on a nonamenable
graph is complicated, since the cardinality of balls grows exponentially fast
with the radius. We propose an algorithm to get a bound from below for this
spectral radius in Cayley graphs with finitely many cone types (including for
instance hyperbolic groups). In the genus $2$ surface group, it improves by an
order of magnitude the previous best bound, due to Bartholdi.
