{"title":"Large Fluctuations in Amplifying Graphs","authors":"Stefano Lepri","doi":"10.1142/s0219477524500159","DOIUrl":null,"url":null,"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.","PeriodicalId":55155,"journal":{"name":"Fluctuation and Noise Letters","volume":"2 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fluctuation and Noise Letters","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0219477524500159","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Fluctuation and Noise Letters (FNL) is unique. It is the only specialist journal for fluctuations and noise, and it covers that topic throughout the whole of science in a completely interdisciplinary way. High standards of refereeing and editorial judgment are guaranteed by the selection of Editors from among the leading scientists of the field.
FNL places equal emphasis on both fundamental and applied science and the name "Letters" is to indicate speed of publication, rather than a limitation on the lengths of papers. The journal uses on-line submission and provides for immediate on-line publication of accepted papers.
FNL is interested in interdisciplinary articles on random fluctuations, quite generally. For example: noise enhanced phenomena including stochastic resonance; 1/f noise; shot noise; fluctuation-dissipation; cardiovascular dynamics; ion channels; single molecules; neural systems; quantum fluctuations; quantum computation; classical and quantum information; statistical physics; degradation and aging phenomena; percolation systems; fluctuations in social systems; traffic; the stock market; environment and climate; etc.
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