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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The cavity and TAP equations are high-dimensional systems of nonlinearequations of the local magnetization in the Sherrington-Kirkpatrick model. Inthe seminal work [Comm. Math. Phys., 325(1):333-366, 2014], Bolthausenintroduced an iterative scheme that produces an asymptotic solution to the TAPequations if the model lies inside the Almeida-Thouless transition line.However, it was unclear if this asymptotic solution coincides with the localmagnetization. In this work, motivated by the cavity equations, we introduce anew iterative scheme and establish a weak law of large numbers. We show thatour new scheme is asymptotically the same as the so-called Approximate MessagePassing algorithm, a generalization of Bolthausen's iteration, that has beenpopularly adapted in compressed sensing, Bayesian inferences, etc. Based onthis, we confirm that our cavity iteration and Bolthausen's scheme bothconverge to the local magnetization as long as the overlap is locally uniformlyconcentrated.

On convergence of the cavity and Bolthausen's TAP iterations to the local magnetization