{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:44:36Z","timestamp":1776797076875,"version":"3.51.2"},"reference-count":41,"publisher":"American Mathematical Society (AMS)","issue":"288","license":[{"start":{"date-parts":[[2015,3,25]],"date-time":"2015-03-25T00:00:00Z","timestamp":1427241600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"d\">\n                        <mml:semantics>\n                          <mml:mi>d<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states, and by using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical coarse-graining schemes that are accompanied by a posteriori error estimates for lattice systems with short- and long-range interactions.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2014-02806-8","type":"journal-article","created":{"date-parts":[[2014,3,25]],"date-time":"2014-03-25T09:11:06Z","timestamp":1395738666000},"page":"1757-1793","source":"Crossref","is-referenced-by-count":4,"title":["Coarse-graining schemes for stochastic lattice systems with short and long-range interactions"],"prefix":"10.1090","volume":"83","author":[{"given":"Markos","family":"Katsoulakis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Petr","family":"Plech\u00e1\u010d","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luc","family":"Rey-Bellet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dimitrios","family":"Tsagkarogiannis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2014,3,25]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"Reinier L. 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