# Stochastic melonic kinetics with random initial conditions Source: [Stochastic melonic kinetics with random initial conditions]() Collection index: [llms.txt]() Data updated: 2025-10-27T04:21:12.031Z Authors: Bio Wahabou Kpera, Vincent Lahoche, Dine Ousmane Samary Published: 2023-02-06T15:57:29.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()