{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T13:17:46Z","timestamp":1772371066375,"version":"3.50.1"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2018,5,21]],"date-time":"2018-05-21T00:00:00Z","timestamp":1526860800000},"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":[[2018,11]]},"abstract":"<jats:p>We develop a method to compute the generating function of the number of vertices inside certain regions of the Uniform Infinite Planar Triangulation (UIPT). The computations are mostly combinatorial in flavour and the main tool is the decomposition of the UIPT into layers, called the skeleton decomposition, introduced by Krikun [20]. In particular, we get explicit formulas for the generating functions of the number of vertices inside hulls (or completed metric balls) centred around the root, and the number of vertices inside geodesic slices of these hulls. We also recover known results about the scaling limit of the volume of hulls previously obtained by Curien and Le Gall by studying the peeling process of the UIPT in [17].<\/jats:p>","DOI":"10.1017\/s0963548318000093","type":"journal-article","created":{"date-parts":[[2018,5,21]],"date-time":"2018-05-21T09:27:26Z","timestamp":1526894846000},"page":"946-973","source":"Crossref","is-referenced-by-count":4,"title":["Volumes in the Uniform Infinite Planar Triangulation: From Skeletons to Generating Functions"],"prefix":"10.1017","volume":"27","author":[{"given":"LAURENT","family":"M\u00c9NARD","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,5,21]]},"reference":[{"key":"S0963548318000093_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-003-0932-3"},{"key":"S0963548318000093_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511524417"},{"key":"S0963548318000093_ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-005-0424-4"},{"key":"S0963548318000093_ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s11511-013-0096-8"},{"key":"S0963548318000093_ref28","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v20-4041"},{"key":"S0963548318000093_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-003-0297-8"},{"key":"S0963548318000093_ref21","unstructured":"Krikun M. (2005) Local structure of random quadrangulations. arXiv:math\/0512304v2"},{"key":"S0963548318000093_ref29","unstructured":"Schaeffer G. (1998) Conjugaison d'arbres et cartes combinatoires al\u00e9atoires. PhD thesis, Universit\u00e9 Bordeaux I."},{"key":"S0963548318000093_ref22","doi-asserted-by":"publisher","DOI":"10.1214\/12-AOP792"},{"key":"S0963548318000093_ref30","doi-asserted-by":"publisher","DOI":"10.1016\/0550-3213(95)00010-P"},{"key":"S0963548318000093_ref14","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1981-078-2"},{"key":"S0963548318000093_ref19","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511801655"},{"key":"S0963548318000093_ref23","unstructured":"Le Gall J.-F. (2014) The Brownian map: A universal limit for random planar maps. 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(2015) First-passage percolation and local modifications of distances in random triangulations. arXiv:1511.04264"},{"key":"S0963548318000093_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-013-0212-0"},{"key":"S0963548318000093_ref17","doi-asserted-by":"publisher","DOI":"10.1214\/15-AIHP718"},{"key":"S0963548318000093_ref26","unstructured":"Miermont G. (2014) Aspects of Random Planar Maps, Saint Flour Lecture Notes, in preparation."},{"key":"S0963548318000093_ref11","doi-asserted-by":"crossref","DOI":"10.37236\/1822","article-title":"Planar maps as labeled mobiles","volume":"11","author":"Bouttier","year":"2004","journal-title":"Electron. J. Combin."},{"key":"S0963548318000093_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/14-AIHP657"},{"key":"S0963548318000093_ref27","unstructured":"Miller J. and Sheffield S. 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