{"id":"https://openalex.org/W7223368978","doi":"https://doi.org/10.48550/arxiv.2610.30204","title":"Triple Products of Correlated Multivariate Hermite Polynomials","display_name":"Triple Products of Correlated Multivariate Hermite Polynomials","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223368978","doi":"https://doi.org/10.48550/arxiv.2610.30204"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.30204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30204","pdf_url":"https://arxiv.org/pdf/2610.30204","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/2610.30204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085398441","display_name":"Laura Lyman","orcid":"https://orcid.org/0000-0002-3590-3651","observed_orcids":["https://orcid.org/0000-0002-3590-3651"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lyman, Laura","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5085398441"],"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.7246000170707703,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.7246000170707703,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.17239999771118164,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.021800000220537186,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/triple-product","display_name":"triple product","score":0.8740000128746033}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8406000137329102},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.6794999837875366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6281999945640564},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5442000031471252},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5238000154495239},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4334000051021576},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3968999981880188},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.39410001039505005},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.39079999923706055},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.3885999917984009},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3880999982357025},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.34950000047683716},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.33090001344680786},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.32519999146461487},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31139999628067017},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.2797999978065491},{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.2741999924182892},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.30204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30204","pdf_url":"https://arxiv.org/pdf/2610.30204","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.2610.30204","doi":"https://doi.org/10.48550/arxiv.2610.30204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.30204","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:2610.30204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.30204","pdf_url":"https://arxiv.org/pdf/2610.30204","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223368978.pdf","grobid_xml":"https://content.openalex.org/works/W7223368978.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3171889240","https://openalex.org/W2023038706","https://openalex.org/W2791562034","https://openalex.org/W3035530877","https://openalex.org/W2145748392","https://openalex.org/W2610654596","https://openalex.org/W2804685994","https://openalex.org/W7126036753","https://openalex.org/W6885174824","https://openalex.org/W3005776304"],"abstract_inverted_index":{"Stochastic":[0],"Galerkin":[1,134],"schemes":[2],"(SGS)":[3],"are":[4,60,104,112,157],"used":[5,46,191],"to":[6,9,47,118,124,168,192,211],"approximate":[7],"solutions":[8],"differential":[10],"equations":[11],"with":[12,21,116,213],"stochastic":[13,55],"parameters.":[14,216],"In":[15,170],"particular,":[16],"they":[17],"express":[18],"the":[19,28,38,53,58,62,67,101,119,127,194,206],"solution":[20,39,68],"an":[22,186],"infinite":[23,63],"orthogonal":[24],"functional":[25],"basis":[26,102],"of":[27,36,40,52,66,130,142],"parameter":[29],"space":[30],"and":[31,94,145,163,175],"derive":[32],"a":[33,49],"deterministic":[34,42],"system":[35,43],"PDEs;":[37],"this":[41,171],"can":[44,189],"be":[45,190],"produce":[48],"{surrogate}":[50],"approximation":[51],"original":[54],"equations.":[56],"When":[57],"parameters":[59,99],"correlated,":[61],"series":[64],"representation":[65],"does":[69],"not":[70,137],"provably":[71],"converge":[72],"for":[73,96,150,180],"all":[74],"joint":[75,121],"distributions;":[76],"further,":[77],"classic":[78],"decorrelating":[79],"transformations":[80],"(e.g.,":[81],"Roseblatt)":[82],"often":[83],"introduce":[84,174],"known":[85],"numerical":[86],"instabilities.":[87],"Rahman":[88],"(2017)":[89],"established":[90],"convergence":[91],"in":[92,185],"probability":[93],"distribution":[95],"correlated":[97,214],"{Gaussian}":[98],"when":[100],"functionals":[103],"{multivariate":[105],"Hermite":[106],"polynomials}":[107],"(MHPs),":[108],"where":[109],"these":[110,155],"polynomials":[111],"only":[113],"{weakly":[114],"orthogonal}":[115],"respect":[117],"underlying":[120],"density.":[122],"Due":[123],"weak":[125],"orthogonality,":[126],"$N$th":[128],"moments":[129,156,198],"MHPs":[131],"introduced":[132],"during":[133],"projection":[135],"do":[136],"trivially":[138],"decompose":[139],"into":[140],"products":[141],"one-dimensional":[143],"expectations":[144],"have":[146],"no":[147],"closed-form":[148],"expression":[149],"$N":[151,195],">":[152],"2$;":[153],"consequently,":[154],"typically":[158],"estimated":[159],"via":[160],"brute-force":[161],"sampling":[162],"quickly":[164],"become":[165],"prohibitively":[166],"expensive":[167],"compute.":[169],"paper,":[172],"we":[173],"prove":[176],"several":[177],"foundational":[178],"results":[179,183],"MHPs.":[181],"These":[182],"culminate":[184],"equation":[187],"that":[188],"calculate":[193],"=":[196],"3$":[197],"(triple":[199],"products)":[200],"exactly,":[201],"whose":[202],"implementation":[203],"dramatically":[204],"reduces":[205],"computational":[207],"bottleneck":[208],"otherwise":[209],"inherent":[210],"SGS":[212],"Gaussian":[215]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-24T00:00:00"}
