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

Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used incomputational physics and statistical computing. Yet, their most fundamentalproperties, such as relations between convergence characteristics of theirvarious versions, are not well understood.  In this paper we prove the solidarity of their spectral gaps: if any of therandom scan or $d!$ deterministic scans has a~spectral gap then all of themhave. Our methods rely on geometric interpretation of the Gibbs samplers asalternating projection algorithms and analysis of the rate of convergence inthe von Neumann--Halperin method of cyclic alternating projections.  In addition, we provide a quantitative result: if the spectral gap of therandom scan Gibbs sampler scales polynomially with dimension, so does thespectral gap of any of the deterministic scans.

Solidarity of Gibbs Samplers: the spectral gap