{"id":"https://openalex.org/W7222956479","doi":"https://doi.org/10.48550/arxiv.2610.23775","title":"Polytope Sampling at the Speed of Isoperimetry","display_name":"Polytope Sampling at the Speed of Isoperimetry","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222956479","doi":"https://doi.org/10.48550/arxiv.2610.23775"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23775","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23775","pdf_url":"https://arxiv.org/pdf/2610.23775","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.23775","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000908733","display_name":"Anming Gu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gu, Anming","raw_affiliation_strings":["University of Texas at Austin ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin ,","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071924017","display_name":"Bobby Shi","orcid":"https://orcid.org/0000-0001-7850-8291","observed_orcids":["https://orcid.org/0000-0001-7850-8291"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Bobby","raw_affiliation_strings":["Simons Institute for the Theory of Computing ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Simons Institute for the Theory of Computing ,","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101553599","display_name":"Kevin Tian","orcid":"https://orcid.org/0000-0003-0109-9201","observed_orcids":["https://orcid.org/0000-0003-0109-9201","https://orcid.org/0000-0002-9876-3991"]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tian, Kevin","raw_affiliation_strings":["University of Texas at Austin ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin ,","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125313988","display_name":"Hubert Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yang, Hubert","raw_affiliation_strings":["University of Texas at Austin ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Texas at Austin ,","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9570000171661377,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9570000171661377,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.023600000888109207,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.007899999618530273,"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/isoperimetry","display_name":"isoperimetry","score":0.7580000162124634},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.8539999723434448},{"id":"https://openalex.org/keywords/total-variation-distance","display_name":"total variation distance","score":0.9179999828338623},{"id":"https://openalex.org/keywords/poincare-constant","display_name":"Poincar\u00e9 constant","score":0.9290000200271606},{"id":"https://openalex.org/keywords/logarithmic-barrier","display_name":"logarithmic barrier","score":0.8970000147819519},{"id":"https://openalex.org/keywords/sampling-algorithms","display_name":"sampling algorithms","score":0.3889999985694885},{"id":"https://openalex.org/keywords/high-dimensional-sampling","display_name":"high-dimensional sampling","score":0.3720000088214874}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7174000144004822},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6705999970436096},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5763000249862671},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5548999905586243},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5224999785423279},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5062999725341797},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37619999051094055},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36390000581741333},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2896000146865845},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2784999907016754},{"id":"https://openalex.org/C39947850","wikidata":"https://www.wikidata.org/wiki/Q729523","display_name":"Geometric distribution","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25119999051094055},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23775","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23775","pdf_url":"https://arxiv.org/pdf/2610.23775","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.2610.23775","doi":"https://doi.org/10.48550/arxiv.2610.23775","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23775","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.23775","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23775","pdf_url":"https://arxiv.org/pdf/2610.23775","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/W7222956479.pdf","grobid_xml":"https://content.openalex.org/works/W7222956479.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2804844105","https://openalex.org/W4413267947","https://openalex.org/W2782853928","https://openalex.org/W7143505397","https://openalex.org/W7141297784","https://openalex.org/W2765848362","https://openalex.org/W7096437242","https://openalex.org/W7099306501","https://openalex.org/W4403587703","https://openalex.org/W7133384961"],"abstract_inverted_index":{"We":[0],"give":[1],"faster":[2],"algorithms":[3],"for":[4],"sampling":[5],"from":[6],"the":[7,54,81,96,100,106],"uniform":[8,55,101],"distribution":[9,102],"over":[10],"a":[11,23,46],"polytope.":[12],"Our":[13,76],"main":[14],"result":[15],"is":[16,78],"an":[17,73,91],"algorithm":[18],"that,":[19],"when":[20],"applied":[21],"to":[22,44,53,105],"polytope":[24],"with":[25,103],"$m$":[26],"constraints":[27],"in":[28,40],"$n$":[29],"dimensions,":[30],"uses":[31],"$m":[32,58],"\\cdot":[33],"\\mathrm{poly}\\log(\\frac":[34],"m":[35],"\u03b4)$":[36],"iterations,":[37],"each":[38],"running":[39],"time":[41],"$O(mn^{\u03c9-":[42],"1})$,":[43],"return":[45],"sample":[47],"within":[48],"total":[49],"variation":[50],"distance":[51],"$\u03b4$":[52],"distribution.":[56],"When":[57],"=O(n)$":[59],"and":[60,89],"$\u03b4=":[61],"\\mathrm{poly}(\\frac":[62],"1":[63],"n)$,":[64],"our":[65],"runtime":[66],"improves":[67],"upon":[68],"all":[69],"prior":[70],"works":[71],"by":[72],"$\u03a9(n^{2/3})$":[74],"factor.":[75],"sampler":[77],"based":[79],"on":[80],"recent":[82],"\\emph{functional":[83],"stochastic":[84],"localization}":[85],"framework":[86],"of":[87,99],"[GST26],":[88],"achieves":[90],"iteration":[92],"count":[93],"nearly":[94],"matching":[95],"Poincar\u00e9":[97],"constant":[98],"respect":[104],"logarithmic":[107],"barrier.":[108]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2026-10-20T00:00:00"}
