{"id":"https://openalex.org/W7223697658","doi":"https://doi.org/10.48550/arxiv.2610.32570","title":"On Trace Averages and Sharp Asymptotics for Powers of Haar-Unitary Matrices","display_name":"On Trace Averages and Sharp Asymptotics for Powers of Haar-Unitary Matrices","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223697658","doi":"https://doi.org/10.48550/arxiv.2610.32570"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32570","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32570","pdf_url":"https://arxiv.org/pdf/2610.32570","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/2610.32570","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153445825","display_name":"Ayesha Irfan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Irfan, Ayesha","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153445825"],"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/T11716","display_name":"Random Matrices and Applications","score":0.9984999895095825,"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":0.9984999895095825,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/charlier-polynomials","display_name":"Charlier polynomials","score":0.7009999752044678},{"id":"https://openalex.org/keywords/eigenvalue-spacing","display_name":"eigenvalue spacing","score":0.5400000214576721},{"id":"https://openalex.org/keywords/local-eigenvalue-statistics","display_name":"local eigenvalue statistics","score":0.6800000071525574},{"id":"https://openalex.org/keywords/random-matrix-theory","display_name":"random matrix theory","score":0.47699999809265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7864000201225281},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.7222999930381775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5335000157356262},{"id":"https://openalex.org/C2776333733","wikidata":"https://www.wikidata.org/wiki/Q3045336","display_name":"Fredholm determinant","level":2,"score":0.5113000273704529},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4715999960899353},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4593999981880188},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.45170000195503235},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.4366999864578247},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.4072999954223633},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.40230000019073486},{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.37709999084472656},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.3343999981880188},{"id":"https://openalex.org/C64092710","wikidata":"https://www.wikidata.org/wiki/Q387743","display_name":"Poisson summation formula","level":3,"score":0.32910001277923584},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.31209999322891235},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C61836697","wikidata":"https://www.wikidata.org/wiki/Q124743","display_name":"Wronskian","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C131229623","wikidata":"https://www.wikidata.org/wiki/Q977297","display_name":"Trace class","level":3,"score":0.26969999074935913},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.26750001311302185}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32570","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32570","pdf_url":"https://arxiv.org/pdf/2610.32570","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.2610.32570","doi":"https://doi.org/10.48550/arxiv.2610.32570","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32570","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:2610.32570","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32570","pdf_url":"https://arxiv.org/pdf/2610.32570","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/W7223697658.pdf","grobid_xml":"https://content.openalex.org/works/W7223697658.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2834438054"],"related_works":["https://openalex.org/W7099851643","https://openalex.org/W1988806684","https://openalex.org/W2130406775","https://openalex.org/W4417539428","https://openalex.org/W2889522310","https://openalex.org/W1965891563","https://openalex.org/W2142043361","https://openalex.org/W2036510582","https://openalex.org/W7113782109","https://openalex.org/W2378010563"],"abstract_inverted_index":{"For":[0,44,83],"a":[1,19,50,84,107,118],"Haar-distributed":[2],"matrix":[3],"$U":[4],"\\in":[5,16],"U(N)$,":[6],"Rains's":[7],"power-map":[8],"theorem":[9],"represents":[10],"the":[11,54,71,92,97,102,112,131,136],"spectrum":[12,114],"of":[13,21,46,91,115,139],"$U^m$,":[14],"$m":[15],"\\mathbb{N}$,":[17],"as":[18,121],"superposition":[20],"independent":[22],"lower-dimensional":[23],"CUE":[24],"spectra.":[25],"We":[26],"determine":[27],"how":[28],"this":[29],"exact":[30,98],"decomposition":[31],"appears":[32],"in":[33,37,74],"trace":[34,48,73,86],"moments":[35],"and":[36,40],"sharp":[38,67,108],"Gaussian":[39],"Poisson":[41,109],"limit":[42,110],"laws.":[43],"averages":[45],"mixed":[47],"products,":[49],"Charlier--Ewens":[51],"convolution":[52],"separates":[53],"stable":[55],"Wick":[56],"term":[57],"from":[58,77],"its":[59,126],"full":[60],"finite-$N$":[61],"correction.":[62],"A":[63],"Fredholm":[64],"factorisation":[65],"gives":[66],"total-variation":[68],"asymptotics":[69],"for":[70,111],"normalised":[72],"four":[75],"regimes,":[76],"fixed":[78,85,119],"powers":[79],"to":[80],"$m\\geq":[81],"N$.":[82],"power":[87],"$p$,":[88],"coherent":[89],"summation":[90],"leading":[93],"Laguerre":[94],"correction":[95],"yields":[96],"factor":[99],"$e^{2/p}$.":[100],"At":[101],"mean-spacing":[103],"scale,":[104],"we":[105],"obtain":[106],"unfolded":[113],"$U^m$":[116],"on":[117],"interval":[120],"$N,":[122],"m":[123],"\\rightarrow":[124],"\\infty$;":[125],"first-order":[127],"correction,":[128],"obtained":[129],"via":[130],"second":[132],"Charlier":[133],"polynomial,":[134],"quantifies":[135],"residual":[137],"under-dispersion":[138],"local":[140],"eigenvalue":[141],"counts.":[142]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-27T00:00:00"}
