{"id":"https://openalex.org/W2164689216","doi":"https://doi.org/10.1017/s0963548313000102","title":"Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals","display_name":"Expansion in High Dimension for the Growth Constants of Lattice Trees and Lattice Animals","publication_year":2013,"publication_date":"2013-04-15","ids":{"openalex":"https://openalex.org/W2164689216","doi":"https://doi.org/10.1017/s0963548313000102","mag":"2164689216"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548313000102","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548313000102","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037769662","display_name":"Yuri Mej\u00eda Miranda","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"YURI MEJ\u00cdA MIRANDA","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, CanadaV6T 1Z2 (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, CanadaV6T 1Z2 (e-mail:","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007640171","display_name":"Gordon Slade","orcid":"https://orcid.org/0000-0001-9389-9497"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"GORDON SLADE","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, Vancouver, BC, CanadaV6T 1Z2 (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, Vancouver, BC, CanadaV6T 1Z2 (e-mail:","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":0.41,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.6221962,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"4","first_page":"527","last_page":"565"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6947760581970215},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.6379969120025635},{"id":"https://openalex.org/keywords/lattice-constant","display_name":"Lattice constant","score":0.6287460327148438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.535358190536499},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48002901673316956},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3233488202095032},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.2750453054904938},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25367915630340576},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13676583766937256},{"id":"https://openalex.org/keywords/half-integer","display_name":"Half-integer","score":0.1347646713256836}],"concepts":[{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6947760581970215},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.6379969120025635},{"id":"https://openalex.org/C132612359","wikidata":"https://www.wikidata.org/wiki/Q625641","display_name":"Lattice constant","level":3,"score":0.6287460327148438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.535358190536499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48002901673316956},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3233488202095032},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.2750453054904938},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25367915630340576},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13676583766937256},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.1347646713256836},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548313000102","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548313000102","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.756.5247","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.756.5247","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1208.3513.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.8500000238418579}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1504241636","https://openalex.org/W1532766299","https://openalex.org/W1963845823","https://openalex.org/W1964063518","https://openalex.org/W1964270412","https://openalex.org/W1965050447","https://openalex.org/W1965887892","https://openalex.org/W1968876926","https://openalex.org/W1981828140","https://openalex.org/W1984883222","https://openalex.org/W1993924429","https://openalex.org/W2006134961","https://openalex.org/W2009602157","https://openalex.org/W2012068660","https://openalex.org/W2017564435","https://openalex.org/W2020435017","https://openalex.org/W2028811709","https://openalex.org/W2033232471","https://openalex.org/W2039202741","https://openalex.org/W2064104311","https://openalex.org/W2072609575","https://openalex.org/W2082881018","https://openalex.org/W2091569475","https://openalex.org/W2108551278","https://openalex.org/W2136173378","https://openalex.org/W2150631799","https://openalex.org/W2154749881","https://openalex.org/W2171265914","https://openalex.org/W2291353666","https://openalex.org/W2312413878","https://openalex.org/W3103186998","https://openalex.org/W3103449087","https://openalex.org/W4285719527","https://openalex.org/W4388317767"],"related_works":["https://openalex.org/W2073827581","https://openalex.org/W2196182475","https://openalex.org/W2295989747","https://openalex.org/W2224375053","https://openalex.org/W2405995764","https://openalex.org/W3181520510","https://openalex.org/W1979456269","https://openalex.org/W4287102057","https://openalex.org/W4224214042","https://openalex.org/W151168977"],"abstract_inverted_index":{"We":[0],"compute":[1],"the":[2,7,10,25,37,46],"first":[3],"three":[4],"terms":[5],"of":[6,16],"1/dexpansions":[8],"for":[9,45],"growth":[11],"constants":[12],"and":[13,20],"one-point":[14,47],"functions":[15,48],"nearest-neighbour":[17],"lattice":[18,21,27],"trees":[19],"(bond)":[22],"animals":[23],"on":[24,50],"integer":[26],"$\\mathbb{Z}^d$":[28],",":[29],"with":[30,41],"rigorous":[31],"error":[32],"estimates.":[33],"The":[34],"proof":[35],"uses":[36],"lace":[38],"expansion,":[39],"together":[40],"a":[42],"new":[43],"expansion":[44],"based":[49],"inclusion\u2013exclusion.":[51]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
