In this paper, we consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaotic fluctuations in graphs with amplification, Chaos, Solitons & Fractals 139 (2020) 110003]. We determine the conditions for having fat-tailed invariant measures by considering approximate solution of the Perron–Frobenius equation for generic graphs. An analogy with the statistical mechanics of a directed polymer is presented that allows for a physically appealing interpretation of the statistical regimes. The connection between non-Gaussian statistics and the generalized Lyapunov exponents $L(q)$ is illustrated. Finally, some results concerning large graphs are reported.

在本文中，我们考虑了一种在与区间分段线性图相关的图上进行放大的混沌扩散模型 [S. Lepri，放大图中的混沌波动，混沌，孤子和分形 139 (2020) 110003]。我们通过考虑通用图的 Perron-Frobenius 方程的近似解来确定具有厚尾不变测度的条件。与定向聚合物的统计力学进行类比，可以对统计机制进行物理上有吸引力的解释。非高斯统计量与广义李亚普诺夫指数之间的联系$L（q）$已说明。最后，报告了一些有关大图的结果。