{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T16:13:43Z","timestamp":1775837623603,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,10,17]],"date-time":"2016-10-17T00:00:00Z","timestamp":1476662400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Combinatorica"],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s00493-015-2975-4","type":"journal-article","created":{"date-parts":[[2016,10,18]],"date-time":"2016-10-18T06:16:02Z","timestamp":1476771362000},"page":"333-374","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On the scaling limit of finite vertex transitive graphs with large diameter"],"prefix":"10.1007","volume":"37","author":[{"given":"Itai","family":"Benjamini","sequence":"first","affiliation":[]},{"given":"Hilary","family":"Finucane","sequence":"additional","affiliation":[]},{"given":"Romain","family":"Tessera","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,10,17]]},"reference":[{"key":"2975_CR1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/BF01215373","volume":"135","author":"H. Abels","year":"1974","unstructured":"H. Abels: Specker-kompaktifizierungen von lokal kompakten topologischen gruppen, Mathematische Zeitschrift\n135 (1974), 325\u2013361.","journal-title":"Mathematische Zeitschrift"},{"key":"2975_CR2","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/BF00975011","volume":"29","author":"V. N. Berestovsk\u00ed","year":"1988","unstructured":"V. N. Berestovsk\u00ed: Homogeneous manifolds with an intrinsic metric. I, Sibirsk. Mat. Zh.\n29 (1988), 17\u201329.","journal-title":"Sibirsk. Mat. Zh."},{"key":"2975_CR3","first-page":"14","volume":"30","author":"V. N. Berestovsk\u00ed","year":"1989","unstructured":"V. N. Berestovsk\u00ed: Homogeneous manifolds with an intrinsic metric. II, Sibirsk. Mat. Zh.\n30 (1989), 14\u201328.","journal-title":"Sibirsk. Mat. Zh."},{"key":"2975_CR4","volume-title":"GAFA seminar","author":"I. Benjamini","year":"2012","unstructured":"I. Benjamini and O. Schramm: Finite transitive graph embeddings into a hyperbolic metric space must stretch or squeeze, GAFA seminar, Springer LNM (2012), To appear."},{"key":"2975_CR5","unstructured":"I. Benjamini and A. Yadin: Harmonic measure in the presence of a spectral gap, arXiv:1402.0156."},{"key":"2975_CR6","unstructured":"E. Breuillard: Geometry of groups of polynomial growth and shape of large balls, preprint."},{"key":"2975_CR7","volume-title":"J. de l\u2019Institut de Math. de Jussieu","author":"E. Breuillard","year":"2011","unstructured":"E. Breuillard and B. Green: Approximate groups I: the torsion free nilpotent case, J. de l\u2019Institut de Math. de Jussieu 2011."},{"key":"2975_CR8","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s10240-012-0043-9","volume":"116","author":"E. Breuillard","year":"2012","unstructured":"E. Breuillard, B. Green and T. Tao: The structure of approximate groups, Publ. Math. i.h.\u00e8.s.\n116 (2012), 115\u2013221.","journal-title":"Publ. Math. i.h.\u00e8.s."},{"key":"2975_CR9","unstructured":"E. Breuillard and E. Le Donne: On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry, to appear in Proc. Natl. Acad. Sci."},{"key":"2975_CR10","doi-asserted-by":"crossref","first-page":"1008","DOI":"10.1016\/j.aim.2015.11.025","volume":"289","author":"E. Breuillard","year":"2016","unstructured":"E. Breuillard and M. Tointon: Nilprogressions and groups with moderate growth, Adv. Math.\n289 (2016), 1008\u20131055.","journal-title":"Adv. Math."},{"key":"2975_CR11","volume-title":"Grundl. der Math. Wiss.","author":"M. Bridson","year":"1999","unstructured":"M. Bridson and A. Haefliger: Metric Spaces of Non-Positive Curvature, Grundl. der Math. Wiss.\n319, Springer Verlag, 1999."},{"key":"2975_CR12","volume-title":"\u00c9l\u00e8ments de math\u00e8matiques","author":"N. Bourbaki","year":"1982","unstructured":"N. Bourbaki: \u00c9l\u00e8ments de math\u00e8matiques, Groupes et alg\u00e8bres de Lie, Chapitre 9, Springer, 1982."},{"key":"2975_CR13","volume-title":"A Course in Metric Geometry","author":"D. Burago","year":"2001","unstructured":"D. Burago, Y. Burago and S. Ivanov: A Course in Metric Geometry, American Mathematical Society (2001)."},{"key":"2975_CR14","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/S0040-9383(98)00063-9","volume":"39","author":"C. Champetier","year":"2000","unstructured":"C. Champetier: L\u2019espace des groupes de type fini, Topology\n39 (2000), 657\u2013680.","journal-title":"Topology"},{"key":"2975_CR15","doi-asserted-by":"crossref","first-page":"37","DOI":"10.4310\/jdg\/1214342146","volume":"54","author":"J. Cheeger","year":"2000","unstructured":"J. Cheeger and T. H. Colding: On the structure of spaces with Ricci curvature bounded below, III, J. Differential Geom.\n54 (2000), 37\u201374.","journal-title":"J. Differential Geom."},{"key":"2975_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-65780-1","volume-title":"The theory of ultrafilters","author":"W. W. Comfort","year":"1974","unstructured":"W. W. Comfort and S. Negrepontis: The theory of ultrafilters, Berlin, New York, Springer-Verlag, 1974."},{"key":"2975_CR17","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.endm.2006.06.042","volume":"24","author":"M. DeVos","year":"2006","unstructured":"M. DeVos and B. Mohar: Small separations in vertex-transitive graphs, Electronic Notes in Discrete Mathematics\n24 (2006), 165\u2013172.","journal-title":"Electronic Notes in Discrete Mathematics"},{"key":"2975_CR18","unstructured":"G. A. Freiman: Foundations of a structural theory of set addition, translated from the Russian, Translations of Mathematical Monographs, Vol 37, American Mathematical Society, Providence, R. I. (1973), vii+108."},{"key":"2975_CR19","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/BF01389241","volume":"87","author":"K. Fukaya","year":"1987","unstructured":"K. Fukaya: Collapsing of Riemannian manifolds and eigenvalues of the laplace operator, Invent. Math.\n87 (1987), 517\u2013547.","journal-title":"Invent. Math."},{"key":"2975_CR20","volume-title":"Hausdorff convergence of Riemannian manifolds and its applications, Recent topics in differential and analytic geometry","author":"K. Fukaya","year":"1990","unstructured":"K. Fukaya: Hausdorff convergence of Riemannian manifolds and its applications, Recent topics in differential and analytic geometry, 143-238, Adv. Stud. Pure Math. 18-I, Academic Press, Boston, MA, (1990)."},{"key":"2975_CR21","doi-asserted-by":"crossref","first-page":"253","DOI":"10.2307\/2946606","volume":"136","author":"K. Fukaya","year":"1992","unstructured":"K. Fukaya and T. Yamaguchi: The fundamental groups of almost nonnegatively curved manifolds, Annals of Mathematics\n136 (1992), 253\u2013333.","journal-title":"Annals of Mathematics"},{"key":"2975_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4171\/LEM\/59-1-8","volume":"59","author":"T. Gelander","year":"2013","unstructured":"T. Gelander: A metric version of the Jordan-Turing theorem, Enseign. Math.\n59 (2013), 1\u201312.","journal-title":"Enseign. Math."},{"key":"2975_CR23","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF02698687","volume":"53","author":"M. Gromov","year":"1981","unstructured":"M. Gromov: Groups of polynomial growth and expanding maps, Publ. Math. IHES\n53 (1981), 53\u201373.","journal-title":"Publ. Math. IHES"},{"key":"2975_CR24","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/978-3-0348-9210-0_2","volume-title":"Sub-Riemannian Geometry, Progress in Mathematics","author":"M. Gromov","year":"1996","unstructured":"M. Gromov: Carnot-Carath\u00e8odory spaces seen from within, in: Sub-Riemannian Geometry, Progress in Mathematics 144, edited by A. Bellaiche and J-J. Risler, 79\u2013323, Birkauser (1996)."},{"key":"2975_CR25","unstructured":"M. Gromov: Metric structures for Riemannian and non-Riemannian spaces, volume 152 of Progress in Mathematics, Birkh\u00e4user Boston Inc., Boston, MA, 1999. Based on the 1981 French original, with appendices by M. Katz, P. Pansu and S. Semmes."},{"key":"2975_CR26","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF02761236","volume":"43","author":"D. Kazhdan","year":"1982","unstructured":"D. Kazhdan: On \u03b5-representation, Israel J. Math.\n43 (1982), 315\u2013323.","journal-title":"Israel J. Math."},{"key":"2975_CR27","doi-asserted-by":"crossref","first-page":"599","DOI":"10.4310\/CAG.2003.v11.n4.a1","volume":"11","author":"K. Kuwae","year":"2003","unstructured":"K. Kuwae and T. Shioya: Convergence of spectral structures: a functional analytic theory and its applications to spectral geometry, Comm. Anal. Geom.\n11 (2003), 599\u2013673.","journal-title":"Comm. Anal. Geom."},{"key":"2975_CR28","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1002\/jgt.3190080107","volume":"8","author":"P. Lorimer","year":"1984","unstructured":"P. Lorimer: Vertex-transitive graphs: Symmetric graphs of prime valency, Journal of graph theory\n8 (1984), 55\u201368.","journal-title":"Journal of graph theory"},{"key":"2975_CR29","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1090\/S0273-0979-2011-01359-3","volume":"49","author":"A. Lubotsky","year":"2012","unstructured":"A. Lubotsky: Expander Graphs in Pure and Applied Mathematics, Bull. Amer. Math. Soc.\n49 (2012), 113\u2013162.","journal-title":"Bull. Amer. Math. Soc."},{"key":"2975_CR30","first-page":"815","volume":"23","author":"B. Kleiner","year":"2010","unstructured":"B. Kleiner: A new proof of Gromov\u2019s theorem on groups of polynomial growth, Jour. AMS\n23 (2010), 815\u2013829.","journal-title":"Jour. AMS"},{"key":"2975_CR31","volume-title":"Topological transformation groups","author":"D. Montgomery","year":"1955","unstructured":"D. Montgomery and L. Zippin: Topological transformation groups, Interscience Publishers, New York-London, 1955."},{"key":"2975_CR32","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1017\/S0143385700002054","volume":"3","author":"P. Pansu","year":"1983","unstructured":"P. Pansu: Croissance des boules et des g\u00e8od\u00e8siques ferm\u00e8es dans les nilvari\u00e8t\u00e8s, Ergodic Theory Dyn. Syst.\n3 (1983), 415\u2013445.","journal-title":"Ergodic Theory Dyn. Syst."},{"key":"2975_CR33","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1007\/BF01447892","volume":"97","author":"F. Peter","year":"1927","unstructured":"F. Peter and H. Weyl: Die Vollst\u00e4ndigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe, Math. Ann.\n97 (1927), 737\u2013755.","journal-title":"Math. Ann."},{"key":"2975_CR34","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1090\/S0002-9939-2011-11100-6","volume":"140","author":"C. E. Praeger","year":"2012","unstructured":"C. E. Praeger, L. Pyber, P. Spiga and E. Szab\u00f3: The Weiss conjecture for locally primitive graphs with automorphism groups admitting composition factors of bounded rank, Proc. Amer. Math. Soc.\n140 (2012), 2307\u20132318.","journal-title":"Proc. Amer. Math. Soc."},{"key":"2975_CR35","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/BF01876039","volume":"65","author":"I. Z. Ruzsa","year":"1994","unstructured":"I. Z. Ruzsa: Generalized arithmetical progressions and sumsets, Acta Math. Hungar.\n65 (1994), 379\u2013388.","journal-title":"Acta Math. Hungar."},{"key":"2975_CR36","doi-asserted-by":"crossref","first-page":"627","DOI":"10.2140\/apde.2012.5.627","volume":"5","author":"T. Sanders","year":"2012","unstructured":"T. Sanders: On the Bogolyubov-Ruzsa lemma, Anal. PDE\n5 (2012), 627\u2013655.","journal-title":"Anal. PDE"},{"key":"2975_CR37","doi-asserted-by":"crossref","first-page":"1502","DOI":"10.1007\/s00039-010-0096-1","volume":"20","author":"Y. Shalom","year":"2010","unstructured":"Y. Shalom and T. Tao: A finitary version of Gromov\u2019s polynomial growth theorem, Geom. Funct. Anal.\n20 (2010), 1502\u20131547.","journal-title":"Geom. Funct. Anal."},{"key":"2975_CR38","doi-asserted-by":"crossref","first-page":"105","DOI":"10.2307\/1968716","volume":"39","author":"A. M. Turing","year":"1938","unstructured":"A. M. Turing: Finite approximations to Lie groups, Annals of Math.\n39 (1938), 105\u2013111.","journal-title":"Annals of Math."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00493-015-2975-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-015-2975-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-015-2975-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,28]],"date-time":"2017-06-28T07:54:30Z","timestamp":1498636470000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00493-015-2975-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,17]]},"references-count":38,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["2975"],"URL":"https:\/\/doi.org\/10.1007\/s00493-015-2975-4","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10,17]]}}}