The purpose of this note is threefold. First we state a few conjectures that
allow us to rigorously derive a theory which is asymptotic in N (the number of
agents) that describes transients in large arrays of (identical) linear damped
harmonic oscillators in R with completely decentralized nearest neighbor
interaction. We then use the theory to establish that in a certain range of the
parameters transients grow linearly in the number of agents (and faster outside
that range). Finally, in the regime where this linear growth occurs we give the
constant of proportionality as a function of the signal velocities (see [3]) in
each of the two directions. As corollaries we show that symmetric interactions
are far from optimal and that all these results independent of (reasonable)
boundary conditions.Comment: 11 pages, 4 figure