Large Fluctuations in Amplifying Graphs
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916095652265984 |
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| author | Lepri, Stefano |
| author_facet | Lepri, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_01980 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large Fluctuations in Amplifying Graphs Lepri, Stefano Chaotic Dynamics 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. |
| title | Large Fluctuations in Amplifying Graphs |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2301.01980 |