  This paper explores the joint behaviour of the summands of a random walk when
their mean value goes to infinity as its length increases. It is proved that
all the summands must share the same value, which extends previous results in
the context of large exceedances of finite sums of i.i.d. random variables.
Some consequences are drawn pertaining to the local behaviour of a random walk
conditioned on a large deviation constraint on its end value. It is shown that
the sample paths exhibit local oblic segments with increasing size and slope as
the length of the random walk increases.
