{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,24]],"date-time":"2025-12-24T18:12:18Z","timestamp":1766599938193,"version":"3.38.0"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T00:00:00Z","timestamp":1296691200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2011,5]]},"abstract":"<jats:p>In this paper we study planar first-passage percolation (FPP) models on random Delaunay triangulations. In [14], Vahidi-Asl and Wierman showed, using sub-additivity theory, that the rescaled first-passage time converges to a finite and non-negative constant \u03bc. We show a sufficient condition to ensure that \u03bc&gt;0 and derive some upper bounds for fluctuations. Our proofs are based on percolation ideas and on the method of martingales with bounded increments.<\/jats:p>","DOI":"10.1017\/s0963548310000477","type":"journal-article","created":{"date-parts":[[2011,2,3]],"date-time":"2011-02-03T11:18:46Z","timestamp":1296731926000},"page":"435-453","source":"Crossref","is-referenced-by-count":9,"title":["Asymptotics for First-Passage Times on Delaunay Triangulations"],"prefix":"10.1017","volume":"20","author":[{"given":"LEANDRO P. R.","family":"PIMENTEL","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2011,2,3]]},"reference":[{"unstructured":"[11] Pimentel L. P. R. (2004) Competing growth, interfaces and geodesics in first-passage percolation on Voronoi tilings. PhD thesis, IMPA, Rio de Janeiro.","key":"S0963548310000477_ref11"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref7","DOI":"10.1103\/PhysRevLett.56.889"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref3","DOI":"10.1007\/978-3-662-03981-6"},{"key":"S0963548310000477_ref5","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1214\/aop\/1008956685","article-title":"Geodesics and spanning trees for Euclidean first-passage percolation","volume":"29","author":"Howard","year":"2001","journal-title":"Ann. Probab."},{"key":"S0963548310000477_ref4","first-page":"61","volume-title":"Bernoulli, Bayes, Laplace: Anniversary Volume","author":"Hammersley","year":"1965"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref8","DOI":"10.1214\/aoap\/1177005426"},{"key":"S0963548310000477_ref9","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1111\/j.2517-6161.1968.tb00749.x","article-title":"The ergodic theory","volume":"30","author":"Kingman","year":"1968","journal-title":"J. Roy. Statist. Soc. Ser. B"},{"key":"S0963548310000477_ref10","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1214\/aop\/1024404279","article-title":"Domination by product measures","volume":"25","author":"Ligget","year":"1997","journal-title":"Ann. Probab."},{"unstructured":"[13] Pimentel L. P. R. (2010) On Some fundamental aspects of Polyominoes on Random Voronoi Tilings. Preprint, available at: http\/\/arxiv.org\/abs\/1009.3898v1.","key":"S0963548310000477_ref13"},{"unstructured":"[14] Vahidi-Asl M. Q. and Wierman J. C. (1990) First-passage percolation on the Voronoi tessellation and Delaunay triangulation. In Random Graphs 87 ( Karonske M. , Jaworski J. and Rucinski A. , eds), pp. 341\u2013359.","key":"S0963548310000477_ref14"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref6","DOI":"10.1007\/s002200050027"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref12","DOI":"10.1214\/ECP.v11-1210"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref2","DOI":"10.1017\/CBO9781139167383"},{"doi-asserted-by":"publisher","key":"S0963548310000477_ref1","DOI":"10.1090\/S0894-0347-99-00307-0"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548310000477","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,2]],"date-time":"2025-03-02T10:17:11Z","timestamp":1740910631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548310000477\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,3]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,5]]}},"alternative-id":["S0963548310000477"],"URL":"https:\/\/doi.org\/10.1017\/s0963548310000477","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2011,2,3]]}}}