{"id":"https://openalex.org/W3121536188","doi":"https://doi.org/10.1109/tit.2021.3114351","title":"Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensembles","display_name":"Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensembles","publication_year":2021,"publication_date":"2021-09-20","ids":{"openalex":"https://openalex.org/W3121536188","doi":"https://doi.org/10.1109/tit.2021.3114351","mag":"3121536188"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3114351","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3114351","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2101.07464","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038111389","display_name":"Yue M. Lu","orcid":"https://orcid.org/0000-0002-5174-2595"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yue M. Lu","raw_affiliation_strings":["John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA","John A. Paulson School of Engineering & Applied Sciences, Harvard University, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"John A. Paulson School of Engineering & Applied Sciences, Harvard University, Cambridge, MA, USA","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038111389"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02502182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"12","first_page":"8264","last_page":"8272"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9959999918937683,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6572538018226624},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6488184332847595},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.644315779209137},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5033630728721619},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4839628040790558},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47840461134910583},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46687573194503784},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33749669790267944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3281008303165436},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3247227072715759},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13541093468666077},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08207207918167114}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6572538018226624},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6488184332847595},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.644315779209137},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5033630728721619},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4839628040790558},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47840461134910583},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46687573194503784},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33749669790267944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3281008303165436},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3247227072715759},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13541093468666077},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08207207918167114},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3114351","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3114351","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2101.07464","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.07464","pdf_url":"https://arxiv.org/pdf/2101.07464","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2101.07464","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2101.07464","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:3121536188","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2101.07464","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.07464","pdf_url":"https://arxiv.org/pdf/2101.07464","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1576347883","https://openalex.org/W1595409123","https://openalex.org/W1884490694","https://openalex.org/W1974755392","https://openalex.org/W2039778940","https://openalex.org/W2066459155","https://openalex.org/W2073955633","https://openalex.org/W2084661953","https://openalex.org/W2086351984","https://openalex.org/W2092590148","https://openalex.org/W2099551908","https://openalex.org/W2100556411","https://openalex.org/W2120575449","https://openalex.org/W2142949395","https://openalex.org/W2144405862","https://openalex.org/W2158746276","https://openalex.org/W2228653206","https://openalex.org/W2318908986","https://openalex.org/W2610971674","https://openalex.org/W2899702797","https://openalex.org/W2945463326","https://openalex.org/W2957821713","https://openalex.org/W2962714615","https://openalex.org/W2963886912","https://openalex.org/W2964303560","https://openalex.org/W3012452232","https://openalex.org/W3022136271","https://openalex.org/W3023124831","https://openalex.org/W3080250514","https://openalex.org/W3098848552","https://openalex.org/W3113714439","https://openalex.org/W4320800818","https://openalex.org/W6633240241","https://openalex.org/W6683110664","https://openalex.org/W6743578797","https://openalex.org/W6782558979"],"related_works":["https://openalex.org/W3200233003","https://openalex.org/W2949384808","https://openalex.org/W3102670196","https://openalex.org/W2951592057","https://openalex.org/W2963304612","https://openalex.org/W3004722026","https://openalex.org/W3163957220","https://openalex.org/W2611887225","https://openalex.org/W3006312067","https://openalex.org/W3163275449","https://openalex.org/W2066130115","https://openalex.org/W2606570433","https://openalex.org/W2044450349","https://openalex.org/W3209221487","https://openalex.org/W2911420586","https://openalex.org/W2879713770","https://openalex.org/W2952203472","https://openalex.org/W2953064603","https://openalex.org/W2962872625","https://openalex.org/W2582191739"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,45,228],"new":[4,207,229],"algorithm,":[5],"named":[6],"Householder":[7,126],"Dice":[8],"(HD),":[9],"for":[10],"simulating":[11],"dynamics":[12],"on":[13],"dense":[14,46],"random":[15,28,99,237],"matrix":[16,55,100,137],"ensembles":[17],"with":[18,108,176],"rotational":[19],"invariance.":[20],"Examples":[21],"include":[22],"the":[23,26,39,57,89,97,105,109,112,132,136,142,147,155,184,202,206,221,224,233],"Gaussian":[24],"ensemble,":[25,30,58],"Haar-distributed":[27],"orthogonal":[29,129],"and":[31,72,121,151,166,215],"their":[32],"complex-valued":[33],"counterparts.":[34],"A":[35],"\u201cdirect\u201d":[36],"approach":[37],"to":[38,210],"simulation,":[40],"where":[41],"one":[42],"first":[43],"generates":[44],"<inline-formula":[47,62,79,159,167,177,189],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[48,63,80,160,168,178,190],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[49,64,81,161,169,179,191],"<tex-math":[50,65,82,162,170,180,192],"notation=\"LaTeX\">$n":[51],"\\times":[52],"n$":[53,195],"</tex-math></inline-formula>":[54,68,85,165,173,182,196],"from":[56],"requires":[59],"at":[60],"least":[61],"notation=\"LaTeX\">$\\mathcal":[66,83,163,171],"{O}(n^{2})$":[67,84],"resource":[69],"in":[70,101,204,213,232],"space":[71],"time.":[73],"The":[74,149],"HD":[75,156,225],"algorithm":[76,117,157,208,226],"overcomes":[77],"this":[78,115],"bottleneck":[86],"by":[87,146],"using":[88],"principle":[90],"of":[91,114,124,135,154,186,223,235],"deferred":[92],"decisions:":[93],"rather":[94],"than":[95],"fixing":[96],"entire":[98],"advance,":[102],"it":[103],"lets":[104],"randomness":[106],"unfold":[107],"dynamics.":[110,148],"At":[111],"heart":[113],"matrix-free":[116],"is":[118,199],"an":[119],"adaptive":[120],"recursive":[122],"construction":[123],"(random)":[125],"reflectors.":[127],"These":[128],"transformations":[130],"exploit":[131],"group":[133],"symmetry":[134],"ensembles,":[138],"while":[139],"simultaneously":[140],"maintaining":[141],"statistical":[143],"correlations":[144],"induced":[145],"memory":[150,216],"computation":[152],"costs":[153],"are":[158],"{O}(nT)$":[164],"{O}(nT^{2})$":[172],",":[174,197],"respectively,":[175],"notation=\"LaTeX\">$T$":[181],"being":[183],"number":[185],"iterations.":[187],"When":[188],"notation=\"LaTeX\">$T":[193],"\\ll":[194],"which":[198],"nearly":[200],"always":[201],"case":[203],"practice,":[205],"leads":[209],"significant":[211],"reductions":[212],"runtime":[214],"footprint.":[217],"Numerical":[218],"results":[219],"demonstrate":[220],"promise":[222],"as":[227],"computational":[230],"tool":[231],"study":[234],"high-dimensional":[236],"systems.":[238]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
