{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T21:35:25Z","timestamp":1753738525224},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T00:00:00Z","timestamp":1642377600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider a variant of a classical coverage process, the Boolean model in<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900221000346_inline1.png\" \/><jats:tex-math>$\\mathbb{R}^d$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Previous efforts have focused on convergence of the unoccupied region containing the origin to a well-studied limit<jats:italic>C<\/jats:italic>. We study the intersection of sets centered at points of a Poisson point process confined to the unit ball. Using a coupling between the intersection model and the original Boolean model, we show that the scaled intersection converges weakly to the same limit<jats:italic>C<\/jats:italic>. Along the way, we present some tools for studying statistics of a class of intersection models.<\/jats:p>","DOI":"10.1017\/jpr.2021.34","type":"journal-article","created":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T14:14:38Z","timestamp":1642428878000},"page":"131-151","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["Intersections of random sets"],"prefix":"10.1017","volume":"59","author":[{"given":"Jacob","family":"Richey","sequence":"first","affiliation":[]},{"given":"Amites","family":"Sarkar","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,1,17]]},"reference":[{"key":"S0021900221000346_ref25","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.52.5.1157"},{"key":"S0021900221000346_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176992809"},{"key":"S0021900221000346_ref8","unstructured":"[8] Cannone, C. (2017). A short note on Poisson tail bounds. 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