{"id":"https://openalex.org/W7163174330","doi":"https://doi.org/10.48550/arxiv.2606.01218","title":"Finite-Resolution Information from Collision Statistics","display_name":"Finite-Resolution Information from Collision Statistics","publication_year":2026,"publication_date":"2026-05-31","ids":{"openalex":"https://openalex.org/W7163174330","doi":"https://doi.org/10.48550/arxiv.2606.01218"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.01218","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.01218","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.01218","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137693560","display_name":"Alexander J. Gates","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gates, Alexander J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5137693560"],"corresponding_institution_ids":[],"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.23589999973773956,"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"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.23589999973773956,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.13819999992847443,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.1185000017285347,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/collision","display_name":"Collision","score":0.7921000123023987},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6273999810218811},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.5336999893188477},{"id":"https://openalex.org/keywords/coincidence","display_name":"Coincidence","score":0.5054000020027161},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4970000088214874},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.4814999997615814},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.40639999508857727}],"concepts":[{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.7921000123023987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7516000270843506},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6273999810218811},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.5336999893188477},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.5054000020027161},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.4814999997615814},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41749998927116394},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.4047999978065491},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3578000068664551},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.328000009059906},{"id":"https://openalex.org/C87538441","wikidata":"https://www.wikidata.org/wiki/Q389463","display_name":"Collision attack","level":5,"score":0.32739999890327454},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.326200008392334},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.31450000405311584},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3052000105381012},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.2782999873161316},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.2599000036716461},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.01218","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.01218","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,"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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.01218","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.01218","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Collision":[0],"statistics":[1],"provide":[2],"a":[3,12,170],"finite-resolution":[4,104,171],"view":[5,172],"of":[6,15,30,74,102,173],"information":[7,168,185],"by":[8,71],"measuring":[9],"how":[10],"often":[11],"fixed":[13,94],"number":[14],"independent":[16],"samples":[17],"fall":[18],"on":[19],"the":[20,28,72,75,80,103,145],"same":[21],"state.":[22],"These":[23],"directly":[24],"countable":[25],"quantities":[26],"form":[27],"basis":[29],"integer-order":[31],"R\u00e9nyi":[32,38,76,162],"entropies.":[33],"Here,":[34],"we":[35,120],"use":[36],"low-order":[37,177],"entropies":[39],"to":[40],"approximate":[41],"Shannon":[42,81,114,130,164],"entropy":[43,77,115],"and":[44,132,148,154,166,182],"mutual":[45,117,167],"information,":[46,174],"while":[47],"characterizing":[48],"what":[49],"is":[50,69,180,186],"necessarily":[51],"lost":[52],"when":[53,176,183],"only":[54],"finitely":[55],"many":[56],"collision":[57,95,124,135,160],"moments":[58,125],"are":[59],"used.":[60],"We":[61,83],"derive":[62],"interpolation-error":[63],"bounds":[64],"showing":[65],"that":[66,122,133],"approximation":[67],"error":[68,88],"controlled":[70],"shape":[73],"path":[78],"near":[79],"point.":[82],"also":[84],"separate":[85],"this":[86],"deterministic":[87,111],"from":[89,113],"finite-sample":[90],"estimation":[91,101],"error:":[92],"for":[93],"order,":[96],"increasing":[97,134],"sample":[98],"size":[99],"improves":[100],"target":[105],"but":[106],"does":[107],"not":[108,127],"eliminate":[109],"its":[110],"difference":[112],"or":[116],"information.":[118],"Finally,":[119],"show":[121],"finite":[123],"do":[126],"generally":[128],"identify":[129],"entropy,":[131,163],"order":[136],"shifts":[137],"sensitivity":[138],"toward":[139],"high-probability":[140],"events.":[141],"Numerical":[142],"experiments":[143],"illustrate":[144],"approximation--estimation":[146],"tradeoff":[147],"compare":[149],"collision-based":[150],"approximations":[151],"with":[152],"plug-in":[153],"Miller--Madow":[155],"estimators.":[156],"The":[157],"framework":[158],"links":[159],"counts,":[161],"limits,":[165],"through":[169],"clarifying":[175],"coincidence":[178],"structure":[179],"informative":[181],"irreducible":[184],"lost.":[187]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-03T00:00:00"}