{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T13:11:14Z","timestamp":1748524274149},"reference-count":24,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2021]]},"abstract":"<p style='text-indent:20px;'>In this paper we provide converge rates for the homogenization of the Poisson problem with Dirichlet boundary conditions in a randomly perforated domain of <inline-formula><tex-math id=\"M1\">\\begin{document}$ \\mathbb{R}^d $\\end{document}<\/tex-math><\/inline-formula>, <inline-formula><tex-math id=\"M2\">\\begin{document}$ d \\geqslant 3 $\\end{document}<\/tex-math><\/inline-formula>. We assume that the holes that perforate the domain are spherical and are generated by a rescaled marked point process <inline-formula><tex-math id=\"M3\">\\begin{document}$ (\\Phi, \\mathcal{R}) $\\end{document}<\/tex-math><\/inline-formula>. The point process <inline-formula><tex-math id=\"M4\">\\begin{document}$ \\Phi $\\end{document}<\/tex-math><\/inline-formula> generating the centres of the holes is either a Poisson point process or the lattice <inline-formula><tex-math id=\"M5\">\\begin{document}$ \\mathbb{Z}^d $\\end{document}<\/tex-math><\/inline-formula>; the marks <inline-formula><tex-math id=\"M6\">\\begin{document}$ \\mathcal{R} $\\end{document}<\/tex-math><\/inline-formula> generating the radii are unbounded i.i.d random variables having finite <inline-formula><tex-math id=\"M7\">\\begin{document}$ (d-2+\\beta) $\\end{document}<\/tex-math><\/inline-formula>-moment, for <inline-formula><tex-math id=\"M8\">\\begin{document}$ \\beta &gt; 0 $\\end{document}<\/tex-math><\/inline-formula>. We study the rate of convergence to the homogenized solution in terms of the parameter <inline-formula><tex-math id=\"M9\">\\begin{document}$ \\beta $\\end{document}<\/tex-math><\/inline-formula>. We stress that, for low values of <inline-formula><tex-math id=\"M10\">\\begin{document}$ \\beta $\\end{document}<\/tex-math><\/inline-formula>, the balls generating the holes may overlap with overwhelming probability.<\/p><\/jats:p>","DOI":"10.3934\/nhm.2021009","type":"journal-article","created":{"date-parts":[[2021,4,21]],"date-time":"2021-04-21T10:56:27Z","timestamp":1619002587000},"page":"341","source":"Crossref","is-referenced-by-count":4,"title":["Convergence rates for the homogenization of the Poisson problem in randomly perforated domains"],"prefix":"10.3934","volume":"16","author":[{"given":"Arianna","family":"Giunti","sequence":"first","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2021009-1","doi-asserted-by":"publisher","unstructured":"G. Allaire.Homogenization of the Navier-Stokes equations in open sets perforated with tiny holes. I. Abstract framework, a volume distribution of holes, Arch. Rational Mech. 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