{"id":"https://openalex.org/W7216086300","doi":"https://doi.org/10.48550/arxiv.2610.02007","title":"Approximation and computation of the geodesic Sinkhorn distance","display_name":"Approximation and computation of the geodesic Sinkhorn distance","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7216086300","doi":"https://doi.org/10.48550/arxiv.2610.02007"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.02007","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02007","pdf_url":"https://arxiv.org/pdf/2610.02007","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/2610.02007","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011294000","display_name":"Hugo Lavenant","orcid":"https://orcid.org/0000-0002-2597-1124","observed_orcids":["https://orcid.org/0000-0002-2597-1124"]},"institutions":[{"id":"https://openalex.org/I71209653","display_name":"Bocconi University","ror":"https://ror.org/05crjpb27","country_code":"IT","type":"education","lineage":["https://openalex.org/I71209653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lavenant, Hugo","raw_affiliation_strings":["Bocconi University , Department of Decision Sciences and BIDSA , Via Sarfatti 25 , 20136 Milan , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bocconi University , Department of Decision Sciences and BIDSA , Via Sarfatti 25 , 20136 Milan , Italy","institution_ids":["https://openalex.org/I71209653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5097357799","display_name":"Jonas Luckhardt","orcid":"https://orcid.org/0009-0002-3057-4446","observed_orcids":["https://orcid.org/0009-0002-3057-4446"]},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Luckhardt, Jonas","raw_affiliation_strings":["Georg-August -Universit\u00e4t G\u00f6ttingen , Institute for Computer Science , Goldschmidstra\u00dfe 7 , 37077 , G\u00f6ttingen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georg-August -Universit\u00e4t G\u00f6ttingen , Institute for Computer Science , Goldschmidstra\u00dfe 7 , 37077 , G\u00f6ttingen , Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059838227","display_name":"Bernhard Schmitzer","orcid":"https://orcid.org/0000-0002-6146-8833","observed_orcids":["https://orcid.org/0000-0002-6146-8833"]},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Schmitzer, Bernhard","raw_affiliation_strings":["Georg-August -Universit\u00e4t G\u00f6ttingen , Institute for Computer Science , Goldschmidstra\u00dfe 7 , 37077 , G\u00f6ttingen , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georg-August -Universit\u00e4t G\u00f6ttingen , Institute for Computer Science , Goldschmidstra\u00dfe 7 , 37077 , G\u00f6ttingen , Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"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":1,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":9.999999747378752e-05,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sinkhorn-divergence","display_name":"Sinkhorn divergence","score":0.8289999961853027},{"id":"https://openalex.org/keywords/geodesic-distance","display_name":"geodesic distance","score":0.7950000166893005},{"id":"https://openalex.org/keywords/entropic-optimal-transport","display_name":"entropic optimal transport","score":0.9739999771118164},{"id":"https://openalex.org/keywords/gromov-hausdorff-convergence","display_name":"Gromov-Hausdorff convergence","score":0.9739999771118164},{"id":"https://openalex.org/keywords/gamma-convergence","display_name":"Gamma-convergence","score":0.8259999752044678}],"concepts":[{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.8388000130653381},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8057000041007996},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6930999755859375},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6097000241279602},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5464000105857849},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.5307000279426575},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.45579999685287476},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4530999958515167},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.44110000133514404},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4318000078201294},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.41359999775886536},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.3889000117778778},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.36800000071525574},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.29580000042915344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28690001368522644},{"id":"https://openalex.org/C181104567","wikidata":"https://www.wikidata.org/wiki/Q761383","display_name":"Riemannian geometry","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C2777634741","wikidata":"https://www.wikidata.org/wiki/Q768993","display_name":"Wasserstein metric","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27489998936653137},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2689000070095062},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.25360000133514404},{"id":"https://openalex.org/C127104897","wikidata":"https://www.wikidata.org/wiki/Q5454858","display_name":"Fisher information metric","level":4,"score":0.25189998745918274},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.02007","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02007","pdf_url":"https://arxiv.org/pdf/2610.02007","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.2610.02007","doi":"https://doi.org/10.48550/arxiv.2610.02007","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.02007","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:2610.02007","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.02007","pdf_url":"https://arxiv.org/pdf/2610.02007","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":[{"id":"https://openalex.org/G317969142","display_name":"Numerische Analyse und Verallgemeinerungen f\u00fcr Optimalen Transport","funder_award_id":"403056140","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7216086300.pdf","grobid_xml":"https://content.openalex.org/works/W7216086300.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415435147","https://openalex.org/W7213327304","https://openalex.org/W2620318602","https://openalex.org/W2897105053","https://openalex.org/W4387440060","https://openalex.org/W3120509864","https://openalex.org/W2905908122","https://openalex.org/W3034574626","https://openalex.org/W2784115536","https://openalex.org/W3172480780"],"abstract_inverted_index":{"In":[0,49],"[H.":[1],"Lavenant,":[2],"J.":[3],"Luckhardt,":[4],"G.":[5],"Mordant,":[6],"B.":[7],"Schmitzer,":[8],"L.":[9],"Tamanini,":[10],"The":[11],"Riemannian":[12,29],"geometry":[13],"of":[14,35,66,71,78,86,109],"Sinkhorn":[15,46],"divergences.":[16],"Ann.":[17],"Inst.":[18],"H.":[19],"Poincar\u00e9":[20],"Anal.":[21],"Non":[22],"Lin\u00e9aire":[23],"43":[24],"(2026)]":[25],"we":[26,53,62,83],"introduced":[27],"a":[28],"metric":[30,68],"$\\mathsf{d}_S$":[31],"on":[32],"the":[33,45,50,67,79,87,95],"space":[34],"probability":[36],"distributions":[37],"obtained":[38],"from":[39,44],"entropic":[40],"optimal":[41],"transport,":[42],"specifically":[43],"divergence":[47],"$S_\\varepsilon$.":[48],"present":[51],"work":[52],"discuss":[54],"how":[55],"to":[56,94,106],"approximate":[57],"and":[58,69,102],"compute":[59,107],"$\\mathsf{d}_S$.":[60,99,110],"Spatially,":[61],"prove":[63],"Gromov--Hausdorff":[64],"convergence":[65,70],"geodesics":[72],"for":[73],"increasingly":[74],"fine":[75],"Eulerian":[76],"discretization":[77,89],"base":[80],"space.":[81],"Temporally,":[82],"show":[84],"$\u0393$-convergence":[85],"chain":[88],"$N":[90],"\\sum_{k=0}^{N-1}":[91],"S_\\varepsilon(\u03bc_k,":[92],"\u03bc_{k+1})$":[93],"energy":[96],"functional":[97],"defining":[98],"We":[100],"deduce":[101],"implement":[103],"numerical":[104],"schemes":[105],"approximations":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-03T00:00:00"}
