  Using a Lorentz invariant deformed string/gauge duality model at finite
temperature we calculate the thermal fluctuation and the corresponding linear
response, verifying the fluctuation-dissipation theorem. The deformed AdS$_5$
is constructed by the insertion of an exponential factor $\exp(k/r^2)$ in the
metric. We also compute the string energy and the mean square displacement in
order to investigate the ballistic and diffusive regimes. Furthermore we have
studied the dissipation and the linear response in the zero temperature
scenario.
