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arXiv · 2301.01980

Large Fluctuations in Amplifying Graphs

Stefano Lepri
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Abstract

We consider a model for chaotic diffusion with amplification on graphs associated with piecewise-linear maps of the interval [S. Lepri, Chaos Solitons & Fractals, 139,110003 (2020)]. 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.

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Stefano Lepri. 2023-01-05. Large Fluctuations in Amplifying Graphs. https://doi.org/10.1142/s021947752450015

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