{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T04:05:32Z","timestamp":1745985932202,"version":"3.40.4"},"reference-count":57,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T00:00:00Z","timestamp":1738627200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the hard-core model on a finite square grid graph with stochastic Glauber dynamics parametrized by the inverse temperature <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S096354832500001X_inline1.png\"\/><jats:tex-math>\n$\\beta$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We investigate how the transition between its two maximum-occupancy configurations takes place in the low-temperature regime <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S096354832500001X_inline2.png\"\/><jats:tex-math>\n$\\beta \\to \\infty$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> in the case of periodic boundary conditions. The hard-core constraints and the grid symmetry make the structure of the critical configurations for this transition, also known as essential saddles, very rich and complex. We provide a comprehensive geometrical characterization of these configurations that together constitute a bottleneck for the Glauber dynamics in the low-temperature limit. In particular, we develop a novel isoperimetric inequality for hard-core configurations with a fixed number of particles and show how the essential saddles are characterized not only by the number of particles but also their geometry.<\/jats:p>","DOI":"10.1017\/s096354832500001x","type":"journal-article","created":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T06:32:52Z","timestamp":1738650772000},"page":"445-485","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Critical configurations of the hard-core model on square grid graphs"],"prefix":"10.1017","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9548-6370","authenticated-orcid":false,"given":"Simone","family":"Baldassarri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0125-4825","authenticated-orcid":false,"given":"Vanessa","family":"Jacquier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6585-4785","authenticated-orcid":false,"given":"Alessandro","family":"Zocca","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,2,4]]},"reference":[{"key":"S096354832500001X_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOP492"},{"key":"S096354832500001X_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-015-1334-6"},{"key":"S096354832500001X_ref35","doi-asserted-by":"publisher","DOI":"10.1063\/1.1697217"},{"key":"S096354832500001X_ref41","doi-asserted-by":"publisher","DOI":"10.4171\/jems\/1398"},{"key":"S096354832500001X_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-014-0549-9"},{"key":"S096354832500001X_ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-020-02618-9"},{"key":"S096354832500001X_ref52","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543272"},{"key":"S096354832500001X_ref31","doi-asserted-by":"publisher","DOI":"10.1002\/rsa.20223"},{"key":"S096354832500001X_ref32","unstructured":"[32] Galvin, D. and Tetali, P. 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