  The dynamics of the localized region of the Lyapunov vector for the largest
Lyapunov exponent is discussed in quasi-one-dimensional hard-disk systems at
low density. We introduce a hopping rate to quantitatively describe the
movement of the localized region of this Lyapunov vector, and show that it is a
decreasing function of hopping distance, implying spatial correlation of the
localized regions. This behavior is explained quantitatively by a brick
accumulation model derived from hard-disk dynamics in the low density limit, in
which hopping of the localized Lyapunov vector is represented as the movement
of the highest brick position. We also give an analytical expression for the
hopping rate, which is obtained us a sum of probability distributions for brick
height configurations between two separated highest brick sites. The results of
these simple models are in good agreement with the simulation results for
hard-disk systems.
