A Bernoulli random walk is a random trajectory starting from 0 and having
i.i.d. increments, each of them being +1 or -1, equally likely. The other
families cited in the title are Bernoulli random walks under various
conditionings. A peak in a trajectory is a local maximum. In this paper, we
condition the families of trajectories to have a given number of peaks. We show
that, asymptotically, the main effect of setting the number of peaks is to
change the order of magnitude of the trajectories. The counting process of the
peaks, that encodes the repartition of the peaks in the trajectories, is also
studied. It is shown that suitably normalized, it converges to a Brownian
bridge which is independent of the limiting trajectory. Applications in terms
of plane trees and parallelogram polyominoes are also provided