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Motivated by these, we consider the design and analysis of couplings of the random walk Metropolis algorithm which scale well with the dimension of the target measure. Methodologically, we introduce a low-rank modification of the synchronous coupling that is provably optimally contractive in standard high-dimensional asymptotic regimes. We expose a shortcoming of the reflection coupling, the state of the art at the time of writing, and we propose a modification which mitigates the issue. Our analysis bridges the gap to the optimal scaling literature and builds a framework of asymptotic optimality which may be of independent interest. We illustrate the applicability of our proposed couplings, and the potential for extending our ideas, with various numerical experiments.<\/jats:p>","DOI":"10.1093\/jrsssb\/qkae113","type":"journal-article","created":{"date-parts":[[2024,12,16]],"date-time":"2024-12-16T08:50:49Z","timestamp":1734339049000},"page":"772-795","source":"Crossref","is-referenced-by-count":0,"title":["Scalable couplings for the random walk Metropolis algorithm"],"prefix":"10.1093","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2203-6525","authenticated-orcid":false,"given":"Tam\u00e1s P","family":"Papp","sequence":"first","affiliation":[{"name":"STOR-i Centre for Doctoral Training, Lancaster University , Lancaster ,","place":["UK"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2429-3157","authenticated-orcid":false,"given":"Chris","family":"Sherlock","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Lancaster 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