  The ubiquitous relativistic jet phenomena associated with black holes play a
major role in high and very-high-energy (VHE) astrophysics. In particular,
observations have demonstrated that blazars show VHE emission with
time-variability from days (in the GeV band) to minutes (in the TeV band),
implying very compact emission regions. The real mechanism able to explain the
particle acceleration process responsible for this emission is still debated,
but magnetic reconnection has been lately discussed as a strong potential
candidate and, in some circumstances, as the only possible one. In this work,
we present the results of three-dimensional special relativistic
magnetohydrodynamic simulations of the development of reconnection events
driven by turbulence induced by current-driven kink instability along a
relativistic jet. We have performed a systematic identification of all
reconnection regions in the system, characterizing their local magnetic field
topology and quantifying the reconnection rates. We obtained average rates of
$0.051\pm0.026$ (in units of the Alfv\'{e}n speed) which are comparable to the
predictions of the theory of turbulence-induced fast reconnection. Detailed
statistical analysis also demonstrated that the fast reconnection events follow
a log-normal distribution, which is a signature of its turbulent origin. To
probe the robustness of our method, we have applied our results to the blazar
Mrk 421. Building a synthetic light curve from the integrated power of the
magnetic reconnection events, we evaluated the time-variability from a power
spectral density analysis, obtaining a good agreement with the observations in
the GeV band. This suggests that turbulent fast magnetic reconnection driven by
kink instability can be a possible process behind the high energy emission
variability phenomena observed in blazars.
