{"id":"https://openalex.org/W7224926280","doi":"https://doi.org/10.5281/zenodo.23804105","title":"A triangular window walk on random binary matrices: a conjectured arcsine limit and a candidate mechanism","display_name":"A triangular window walk on random binary matrices: a conjectured arcsine limit and a candidate mechanism","publication_year":2026,"publication_date":"2026-10-30","ids":{"openalex":"https://openalex.org/W7224926280","doi":"https://doi.org/10.5281/zenodo.23804105"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23804105","doi":"https://doi.org/10.5281/zenodo.23804105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23804105","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23804105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160167981","display_name":"Haowei Luo","orcid":"https://orcid.org/0009-0003-7206-7095","observed_orcids":["https://orcid.org/0009-0003-7206-7095"]},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Luo, Haowei","raw_affiliation_strings":["Beijing Jiaotong University"],"raw_orcid":"https://orcid.org/0009-0003-7206-7095","affiliations":[{"raw_affiliation_string":"Beijing Jiaotong University","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5160167981"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T13500","display_name":"Probability and Statistical Research","score":0.8314999938011169,"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/T13500","display_name":"Probability and Statistical Research","score":0.8314999938011169,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.04899999871850014,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.04179999977350235,"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/arcsine-law","display_name":"arcsine law","score":0.9079999923706055},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"central limit theorem","score":0.5339999794960022},{"id":"https://openalex.org/keywords/monte-carlo-simulation","display_name":"Monte Carlo simulation","score":0.9079999923706055}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8147000074386597},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6148999929428101},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.503000020980835},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.49790000915527344},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4819999933242798},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4553000032901764},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36010000109672546},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3474000096321106},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.33880001306533813},{"id":"https://openalex.org/C50742451","wikidata":"https://www.wikidata.org/wiki/Q1530388","display_name":"Equidistributed sequence","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.290800005197525},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.2515000104904175}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.5281/zenodo.23804105","doi":"https://doi.org/10.5281/zenodo.23804105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23804105","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.23804106","doi":"https://doi.org/10.5281/zenodo.23804106","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23804106","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.23809525","doi":"https://doi.org/10.5281/zenodo.23809525","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23809525","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.23910529","doi":"https://doi.org/10.5281/zenodo.23910529","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23910529","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.23804105","doi":"https://doi.org/10.5281/zenodo.23804105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23804105","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7017629831","https://openalex.org/W4297842069","https://openalex.org/W2593267378","https://openalex.org/W3215162298","https://openalex.org/W7214126514","https://openalex.org/W2913165507","https://openalex.org/W4385487782","https://openalex.org/W3187348998","https://openalex.org/W3212950837","https://openalex.org/W1511872106"],"abstract_inverted_index":{"A":[0,131],"deterministic":[1],"map":[2],"is":[3,43,129,139],"defined":[4],"on":[5,17],"n\u00d72":[6],"binary":[7],"matrices":[8],"with":[9,82,116,135,141],"\u2308n/2\u2309":[10],"ones":[11],"per":[12],"column.":[13],"An":[14],"ant":[15],"walks":[16],"the":[18,26,40,52,56,60,64,73,79,86,97,110,136],"triangular":[19],"lattice":[20],"of":[21,34,48,88,101],"intervals;":[22],"two":[23],"comparisons":[24],"inside":[25],"window":[27],"\u2014":[28,45],"whether":[29,39],"its":[30,35],"mean":[31],"exceeds":[32],"that":[33,144],"first":[36],"half,":[37],"and":[38,59,109,121],"lag-one":[41],"autocorrelation":[42,105],"positive":[44],"select":[46],"one":[47],"four":[49],"moves.":[50],"Leaving":[51],"region":[53],"cuts":[54],"off":[55],"smaller":[57],"triangle":[58],"walk":[61],"restarts;":[62],"reaching":[63],"diagonal":[65],"produces":[66],"a":[67,89],"singular":[68,90],"row":[69,91],"\u03b4.":[70],"We":[71],"conjecture:":[72],"normalised":[74],"position":[75],"X=\u03b4/(n\u22121)":[76],"converges":[77],"to":[78,93,107],"arcsine":[80,137],"law":[81],"standard":[83,99],"deviation":[84,100],"1/\u221a8;":[85],"probability":[87],"tends":[92,106],"about":[94],"0.315,":[95],"convention-dependent;":[96],"residual":[98],"X":[102],"against":[103],"density":[104],"0.23;":[108],"reversal":[111],"rate":[112],"obeys":[113],"s(m)=arccos":[114],"\u03c1(m)/\u03c0":[115],"\u03c1(m)\u22481\u22121/m.":[117],"Exact":[118],"enumeration":[119],"(n\u226412)":[120],"Monte":[122],"Carlo":[123],"(n\u22648192)":[124],"support":[125],"all":[126],"four;":[127],"none":[128],"proved.":[130],"six-link":[132],"mechanism":[133],"consistent":[134],"shape":[138],"described,":[140],"five":[142],"models":[143],"fail.":[145]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-31T00:00:00"}