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

We present a simple, perturbative approach for calculating spectral densitiesfor random matrix ensembles in the thermodynamic limit we call the PerturbativeResolvent Method (PRM). The PRM is based on constructing a linear system ofequations and calculating how the solutions to these equation change inresponse to a small perturbation using the zero-temperature cavity method. Weillustrate the power of the method by providing simple analytic derivations ofthe Wigner Semi-circle Law for symmetric matrices, the Marchenko-Pastur Law forWishart matrices, the spectral density for a product Wishart matrix composed oftwo square matrices, and the Circle and elliptic laws for real random matrices.

The Perturbative Resolvent Method: spectral densities of random matrix ensembles via perturbation theory