{"id":"https://openalex.org/W7225639516","doi":"https://doi.org/10.5281/zenodo.24069930","title":"The relaxation time does not control the normal approximation of stationary additive functionals","display_name":"The relaxation time does not control the normal approximation of stationary additive functionals","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225639516","doi":"https://doi.org/10.5281/zenodo.24069930"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24069930","doi":"https://doi.org/10.5281/zenodo.24069930","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069930","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24069930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041315596","display_name":"Yitzchak Shmalo","orcid":"https://orcid.org/0000-0002-2886-3049","observed_orcids":["https://orcid.org/0000-0002-2886-3049"]},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Shmalo, Yitzchak","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041315596"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.92330002784729,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.92330002784729,"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/T13500","display_name":"Probability and Statistical Research","score":0.03530000150203705,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.03180000185966492,"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/relaxation-time","display_name":"relaxation time","score":0.9319999814033508},{"id":"https://openalex.org/keywords/normal-approximation","display_name":"Gaussian approximation","score":0.6740000247955322},{"id":"https://openalex.org/keywords/kolmogorov-distance","display_name":"Kolmogorov distance","score":0.9620000123977661},{"id":"https://openalex.org/keywords/continuous-time-markov-chains","display_name":"continuous-time Markov chains","score":0.8970000147819519},{"id":"https://openalex.org/keywords/reversible-markov-chains","display_name":"reversible Markov chains","score":0.8159999847412109},{"id":"https://openalex.org/keywords/asymptotic-variance","display_name":"asymptotic variance","score":0.5479999780654907},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"central limit theorem","score":0.5929999947547913},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7522000074386597},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6280999779701233},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6240000128746033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5428000092506409},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5376999974250793},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5074999928474426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4812000095844269},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C62100291","wikidata":"https://www.wikidata.org/wiki/Q1936288","display_name":"Total variation","level":2,"score":0.4203000068664551},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.382099986076355},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.3601999878883362},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3352000117301941},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.32179999351501465},{"id":"https://openalex.org/C17964538","wikidata":"https://www.wikidata.org/wiki/Q1319246","display_name":"Incomplete gamma function","level":3,"score":0.31029999256134033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3075999915599823},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C20538924","wikidata":"https://www.wikidata.org/wiki/Q822139","display_name":"Characteristic function (probability theory)","level":3,"score":0.3009999990463257},{"id":"https://openalex.org/C120488996","wikidata":"https://www.wikidata.org/wiki/Q17016064","display_name":"Variance function","level":3,"score":0.2994000017642975},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29649999737739563},{"id":"https://openalex.org/C2778199601","wikidata":"https://www.wikidata.org/wiki/Q5165476","display_name":"Continuous function (set theory)","level":3,"score":0.2946999967098236},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.2888999879360199},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C2988492214","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary solution","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C153658351","wikidata":"https://www.wikidata.org/wiki/Q746264","display_name":"Constant function","level":3,"score":0.25589999556541443},{"id":"https://openalex.org/C18436578","wikidata":"https://www.wikidata.org/wiki/Q7604346","display_name":"Stationary sequence","level":3,"score":0.2533999979496002}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24069930","doi":"https://doi.org/10.5281/zenodo.24069930","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069930","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24069931","doi":"https://doi.org/10.5281/zenodo.24069931","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069931","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24069930","doi":"https://doi.org/10.5281/zenodo.24069930","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069930","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":null,"license_id":null,"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/W2038879799","https://openalex.org/W7064883600","https://openalex.org/W7096118562","https://openalex.org/W7132835428","https://openalex.org/W4386634449","https://openalex.org/W4321321684","https://openalex.org/W7095967633","https://openalex.org/W7099626584","https://openalex.org/W2144184937","https://openalex.org/W7225653687"],"abstract_inverted_index":{"Let":[0],"$X$":[1],"be":[2,24],"a":[3,25,65,88,96],"finite":[4],"irreducible":[5],"reversible":[6],"Markov":[7],"chain":[8,89],"in":[9],"continuous":[10],"time":[11,14],"with":[12,30,93,105,110],"relaxation":[13],"$\\tau_2$,":[15],"started":[16],"from":[17],"its":[18,28],"stationary":[19],"distribution,":[20],"and":[21,33,40,57,69,84,95,102],"let":[22],"$g$":[23,98],"function":[26,66,97],"on":[27,90],"states":[29,92],"mean":[31,100],"$0$":[32,75,101],"variance":[34,55,103],"$1$":[35,104],"under":[36],"that":[37,72,108],"distribution.":[38],"Aldous":[39],"Fill":[41],"asked":[42],"whether":[43],"the":[44,53,58,118,127],"Kolmogorov":[45],"distance":[46,119],"between":[47],"$\\int_0^tg(X_u)\\,du/(\\sigma":[48],"t^{1/2})$,":[49],"where":[50],"$\\sigma^2$":[51],"is":[52,62,79,120,129],"asymptotic":[54],"rate,":[56],"standard":[59],"normal":[60],"law":[61],"bounded":[63],"by":[64],"of":[67,99],"$\\max|g|$":[68],"$t/\\tau_2$":[70],"alone":[71],"tends":[73],"to":[74],"as":[76],"$t/\\tau_2\\to\\infty$.":[77],"It":[78],"not.":[80],"For":[81],"every":[82],"$b\\ge1$":[83],"$s\\ge2b$":[85],"there":[86],"are":[87],"four":[91],"$\\tau_2=1$":[94],"$\\max|g|=b$":[106],"such":[107],"$\\int_0^sg(X_u)\\,du\\le0$":[109],"probability":[111],"at":[112,116,121],"least":[113,122],"$1-4/s$,":[114],"so":[115],"$t=s$":[117],"$1/2-4/s$":[123],"whatever":[124],"positive":[125],"constant":[126],"integral":[128],"divided":[130],"by.":[131]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}