Large Fluctuations in Amplifying Graphs
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 is illustrated. Finally, some results concerning large graphs are reported.
Cite
@article{arxiv.2301.01980,
title = {Large Fluctuations in Amplifying Graphs},
author = {Stefano Lepri},
journal= {arXiv preprint arXiv:2301.01980},
year = {2024}
}
Comments
Submitted to Fluctuation and Noise Letters, special issue Dynamics and Complexity Pisa 22 (DCP22)