English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many solutions for scientific problems rely on finding the first (largest)eigenvalue and eigenvector of a particular matrix. We explore the distributionof the first eigenvector of a symmetric random sparse matrix. To analyze theproperties of the first eigenvalue/vector, we employ a methodology based on thecavity method, a well-established technique in the statistical physics.  A symmetric random sparse matrix in this paper can be regarded as anadjacency matrix for a network. We show that if a network is constructed bynodes that have two different types of degrees then the distribution of itseigenvector has fat tails such as the stable distribution ($\alpha < 2 $) undera certain condition; whereas if a network is constructed with nodes that haveonly one type of degree, the distribution of its first eigenvector becomes theGaussian approximately. The cavity method is used to clarify these results.

Fat-tailed distribution derived from first eigenvector of symmetric random sparse matrix