{"id":"https://openalex.org/W7212299290","doi":"https://doi.org/10.48550/arxiv.2609.10875","title":"Metric Geometry of the Signature Group for $p$-Variation Rough Paths","display_name":"Metric Geometry of the Signature Group for $p$-Variation Rough Paths","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212299290","doi":"https://doi.org/10.48550/arxiv.2609.10875"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.10875","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10875","pdf_url":"https://arxiv.org/pdf/2609.10875","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.10875","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151368067","display_name":"Felix Medwed","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Medwed, Felix","raw_affiliation_strings":["Institute of Mathematics , University of Potsdam , D-14469 Potsdam , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , University of Potsdam , D-14469 Potsdam , Germany","institution_ids":["https://openalex.org/I176453806"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046655235","display_name":"Sylvie Paycha","orcid":"https://orcid.org/0000-0002-6293-2546","observed_orcids":["https://orcid.org/0000-0002-6293-2546"]},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]},{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["DE","NO"],"is_corresponding":false,"raw_author_name":"Paycha, Sylvie","raw_affiliation_strings":["Institute of Mathematics , University of Potsdam , D-14469 Potsdam , Germany","Norwegian University of Science and Technology , NO-7491 Trondheim , Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , University of Potsdam , D-14469 Potsdam , Germany","institution_ids":["https://openalex.org/I176453806"]},{"raw_affiliation_string":"Norwegian University of Science and Technology , NO-7491 Trondheim , Norway","institution_ids":["https://openalex.org/I204778367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055081705","display_name":"Alexander Schmeding","orcid":"https://orcid.org/0000-0001-9463-3674","observed_orcids":["https://orcid.org/0000-0001-9463-3674"]},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Schmeding, Alexander","raw_affiliation_strings":["Institute of Mathematics , University of Potsdam , D-14469 Potsdam , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics , University of Potsdam , D-14469 Potsdam , Germany","institution_ids":["https://openalex.org/I176453806"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.21729999780654907,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.21729999780654907,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.20909999310970306,"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"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.1298000067472458,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/metric-completion","display_name":"metric completion","score":0.5920000076293945},{"id":"https://openalex.org/keywords/rough-paths","display_name":"rough paths","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7107999920845032},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.6956999897956848},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6739000082015991},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.649399995803833},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5878000259399414},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5756000280380249},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5105999708175659},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4787999987602234},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4368000030517578},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35440000891685486},{"id":"https://openalex.org/C166077713","wikidata":"https://www.wikidata.org/wiki/Q1758924","display_name":"Tensor field","level":3,"score":0.3222000002861023},{"id":"https://openalex.org/C53936288","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse limit","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3061999976634979},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2890999913215637},{"id":"https://openalex.org/C8466233","wikidata":"https://www.wikidata.org/wiki/Q757269","display_name":"Metric tensor","level":3,"score":0.26260000467300415}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.10875","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10875","pdf_url":"https://arxiv.org/pdf/2609.10875","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.10875","doi":"https://doi.org/10.48550/arxiv.2609.10875","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.10875","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.10875","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.10875","pdf_url":"https://arxiv.org/pdf/2609.10875","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212299290.pdf","grobid_xml":"https://content.openalex.org/works/W7212299290.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W142666414","https://openalex.org/W1966404902","https://openalex.org/W2139218964","https://openalex.org/W2415461781","https://openalex.org/W2898478723","https://openalex.org/W2964143464","https://openalex.org/W2979511771","https://openalex.org/W3043207359","https://openalex.org/W4241157659","https://openalex.org/W4389500193","https://openalex.org/W4401858236","https://openalex.org/W4402618627","https://openalex.org/W4414637772","https://openalex.org/W7138907107"],"related_works":["https://openalex.org/W2979511771","https://openalex.org/W1960184460","https://openalex.org/W4308648280","https://openalex.org/W4415339758","https://openalex.org/W1566361715","https://openalex.org/W3089250893","https://openalex.org/W7097753793","https://openalex.org/W4404391393","https://openalex.org/W7100580001","https://openalex.org/W2092606244"],"abstract_inverted_index":{"The":[0],"signatures":[1],"of":[2,8,20,34,42,56,81,99,110,119],"$p$-rough":[3],"paths":[4],"form":[5],"a":[6,18,31,59,74],"subgroup":[7,19],"sufficiently":[9],"high-level":[10],"truncated":[11],"tensor":[12,23],"algebras,":[13],"whose":[14],"inverse":[15,40],"limit":[16,41],"is":[17,72],"the":[21,35,39,47,64,69,79,97,100,108,115],"full":[22],"algebra.":[24],"For":[25],"$p":[26],"\\geq":[27],"1$,":[28],"we":[29],"provide":[30],"top-down":[32],"description":[33],"signature":[36,70],"group":[37,71,118],"as":[38],"finite-dimensional":[43],"Carnot--Carath\u00e9odory":[44],"geometries":[45],"in":[46],"$p$-variation":[48],"setting.":[49],"We":[50,94],"show":[51],"that":[52],"every":[53],"compatible":[54],"choice":[55,109],"metrics":[57],"induces":[58],"topological":[60,75],"tree":[61],"structure":[62],"on":[63,107],"inverse-limit":[65,101],"group,":[66],"under":[67],"which":[68],"not":[73],"group.":[76],"This":[77],"extends":[78],"results":[80],"Enrico":[82],"Le":[83],"Donne":[84],"and":[85,103,126],"Roland":[86],"Z\u00fcst":[87],"from":[88],"bounded":[89],"variation":[90],"to":[91],"rough":[92],"paths.":[93],"also":[95],"characterise":[96],"dependence":[98],"groups":[102],"their":[104],"metric":[105],"completions":[106],"metric,":[111],"identifying":[112],"them":[113],"with":[114],"tree-reduced":[116],"path":[117],"Horatio":[120],"Boedihardjo,":[121],"Xiang":[122],"Geng,":[123],"Terry":[124],"Lyons,":[125],"Danyu":[127],"Yang.":[128]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}
