Condensed Matter > Statistical Mechanics
[Submitted on 12 Apr 2022 (v1), last revised 23 Oct 2022 (this version, v2)]
Title:Clusters determine local fluctuations of random walks on graphs
View PDFAbstract:The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph. Fluctuations are quantified by the number of traversals of the random walk across edges during a fixed time window, more precisely, by the corresponding counting statistics. The variance-to-mean ratio of the counting statistics is typically lowered if two end vertices of an edge belong to different clusters as defined by spectral clustering. In particular, we relate the fluctuations to the algebraic connectivity and the Fiedler vector of the graph. Building on these results we suggest a centrality score based on fluctuations of random walks. Our findings imply that local fluctuations of continuous-time Markov processes on discrete state space depend strongly on the global topology of the underlying graph in addition to the specific transition rates.
Submission history
From: Martin Bruderer [view email][v1] Tue, 12 Apr 2022 21:37:28 UTC (44 KB)
[v2] Sun, 23 Oct 2022 10:06:51 UTC (45 KB)
Current browse context:
cond-mat.stat-mech
Change to browse by:
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.