V. Sidoravicius et al., Poisson broken lines process and its application to Bernoulli first passage percolation, ACT APPL MA, 58(1-3), 1999, pp. 311-325
In this note we introduce a process, which we call 'the Poisson broken line
s process', and we compute the intensity of a point process which is obtain
ed by intersecting the Poisson broken lines process with an abscissa axis.
In the second part we apply this result to compute an explicit lower bound
for the time constant of a planar Bernoulli first passage percolation model
with the parameter p < p(c).