Qualitative distribution of the specific gas torque acting on the embedded companion in an accretion disk. The red solid line represents the baseline where the turbulent perturbation is negligible, corresponding to a system governed solely by the deterministic linear torque (T_lin). The blue dashed and green dotted–dashed histograms illustrate the distributions of the chaotic torque under weak and strong turbulence regimes, respectively. Unlike the constant nature of the linear torque, the turbulent torque exhibits highly stochastic behavior characterized by a well-defined Gaussian dispersion. As the turbulence amplitude increases, the standard deviation of the fluctuations broadens significantly. These stochastic fluctuations drive the random-walk orbital evolution that prevents EMRIs from stalling in migration traps. Data and distribution features are modeled after the global HD simulations of Y. Wu et al. (2024).