  The probability laws associated with random tensors or tensor field theories
are traditionally equilibrium distributions. In this paper, we consider a
stochastic point of view, and approach the quantization by a Langevin type
equation. We especially address the low-temperature behavior of the phase
ordering kinetics of a stochastic complex tensor field $T_{i_1\cdots i_d}(x,t)$
of size $N$ and rank $d$ in dimension $D$. The method we propose use the self
averaging property of the tensorial invariants in the large $N$ limit. In this
regime, the dynamics is governed by the melonic sector, whose behavior is
studied in the quenched limit, where the contractions involving $d-1$ indices
self-average around a diagonal matrix proportional to the identity. The
following work especially focuses on the cyclic (i.e. non-branching) melonic
sector, and we study the way that the system returns to the equilibrium regime
regarding the temperature and the shape of the potential. In particular, we
provide a general formula for the transition temperature between these regimes.
The manuscript is accompanied by numerical simulations to support the
theoretical analysis, and essentially aims to open towards this new field of
investigation.
