{"id":"https://openalex.org/W4403364993","doi":"https://doi.org/10.1142/s0218196725500377","title":"Parallel geodesics and minimal stable length of random groups","display_name":"Parallel geodesics and minimal stable length of random groups","publication_year":2025,"publication_date":"2025-08-01","ids":{"openalex":"https://openalex.org/W4403364993","doi":"https://doi.org/10.1142/s0218196725500377"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196725500377","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500377","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2410.07859","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028447325","display_name":"Tsung-Hsuan Tsai","orcid":"https://orcid.org/0000-0002-5780-9260"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]},{"id":"https://openalex.org/I4210146074","display_name":"Analyse, G\u00e9om\u00e9trie et Mod\u00e9lisation","ror":"https://ror.org/03qgt2624","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210142324","https://openalex.org/I4210146074"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Tsung-Hsuan Tsai","raw_affiliation_strings":["Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1, France","ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","AGL - Alg\u00e8bre, g\u00e9om\u00e9trie, logique (France)"],"raw_orcid":"https://orcid.org/0000-0002-5780-9260","affiliations":[{"raw_affiliation_string":"Institut Camille Jordan, Universit\u00e9 Claude Bernard Lyon 1, France","institution_ids":["https://openalex.org/I4210104796","https://openalex.org/I100532134"]},{"raw_affiliation_string":"ICJ - Institut Camille Jordan (B\u00e2t. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX - France)","institution_ids":["https://openalex.org/I4210104796"]},{"raw_affiliation_string":"AGL - Alg\u00e8bre, g\u00e9om\u00e9trie, logique (France)","institution_ids":["https://openalex.org/I4210146074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028447325"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I4210104796","https://openalex.org/I4210146074"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01432009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"08","first_page":"1135","last_page":"1158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12351","display_name":"Geometry and complex manifolds","score":0.9412999749183655,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9179999828338623,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/geodesic","display_name":"Geodesic","score":0.9024816751480103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7000635862350464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6583447456359863},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.5677870512008667},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5379202365875244},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.47558438777923584},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32811471819877625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22882527112960815},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19116780161857605}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.9024816751480103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7000635862350464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6583447456359863},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5677870512008667},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5379202365875244},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.47558438777923584},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32811471819877625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22882527112960815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19116780161857605},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196725500377","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500377","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2410.07859","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.07859","pdf_url":"https://arxiv.org/pdf/2410.07859","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04751962v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04751962","pdf_url":"https://hal.science/hal-04751962/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2424","raw_type":"Preprints, Working Papers, ..."}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2410.07859","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2410.07859","pdf_url":"https://arxiv.org/pdf/2410.07859","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403364993.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2487162673","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2942366970","https://openalex.org/W2807634898","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W2806452552"],"abstract_inverted_index":{"Parallel":[0],"geodesics":[1,32,80],"are":[2],"crucial":[3],"in":[4,15,33,81],"the":[5,9,71,74,90],"study":[6],"of":[7,28,58,77,94],"acylindricity,":[8],"Burnside":[10],"problem,":[11],"and":[12],"canonical":[13],"representatives":[14],"Gromov":[16],"hyperbolic":[17,45],"groups.":[18,83],"In":[19],"this":[20,61],"paper,":[21],"we":[22,63,87],"show":[23,88],"that":[24,89],"for":[25],"any":[26],"pair":[27],"sufficiently":[29],"long":[30],"parallel":[31,79],"a":[34,44,50,95],"random":[35,96],"group":[36,97],"at":[37,98],"density":[38,99],"[Formula:":[39,100,105],"see":[40,101,106],"text]":[41,102],"(which":[42],"is":[43,103],"group),":[46],"one":[47,56],"can":[48],"fit":[49],"van":[51],"Kampen":[52],"diagram":[53],"with":[54],"only":[55,69],"layer":[57],"faces.":[59],"Using":[60],"result,":[62],"provide":[64],"an":[65,85],"upper":[66],"bound,":[67],"depending":[68],"on":[70,73],"density,":[72],"maximal":[75],"number":[76],"pairwise":[78],"such":[82],"As":[84],"application,":[86],"minimal":[91],"stable":[92],"length":[93],"exactly":[104],"text].":[107]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}