{"id":"https://openalex.org/W7225642899","doi":"https://doi.org/10.5281/zenodo.24069906","title":"Occupation sums of the harmonic descent chain and slowly decaying weights","display_name":"Occupation sums of the harmonic descent chain and slowly decaying weights","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225642899","doi":"https://doi.org/10.5281/zenodo.24069906"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24069906","doi":"https://doi.org/10.5281/zenodo.24069906","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069906","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.24069906","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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.7020999789237976,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.7020999789237976,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.24690000712871552,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.012000000104308128,"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/markov-chains","display_name":"Markov chains","score":0.5720000267028809}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8030999898910522},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.7002999782562256},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5687000155448914},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5468999743461609},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5430999994277954},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.4749000072479248},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.46810001134872437},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.4350999891757965},{"id":"https://openalex.org/C203858083","wikidata":"https://www.wikidata.org/wiki/Q188347","display_name":"Harmonic mean","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.3569999933242798},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2680000066757202}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24069906","doi":"https://doi.org/10.5281/zenodo.24069906","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069906","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.24069907","doi":"https://doi.org/10.5281/zenodo.24069907","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069907","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.24069906","doi":"https://doi.org/10.5281/zenodo.24069906","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069906","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225170420","https://openalex.org/W2100659943","https://openalex.org/W4405075383","https://openalex.org/W1542284815","https://openalex.org/W2163709935","https://openalex.org/W2038975260","https://openalex.org/W4414858751","https://openalex.org/W4521549","https://openalex.org/W2049663053","https://openalex.org/W2038209140"],"abstract_inverted_index":{"Let":[0],"$a(n,i)$":[1],"be":[2],"the":[3,6,64,79],"probability":[4],"that":[5,48,78],"harmonic":[7],"descent":[8],"chain":[9,80],"started":[10,81],"at":[11,82,87],"$n$":[12,72,83],"visits":[13,94],"$i$,":[14],"and":[15,19,37,40,59],"$a(i)=\\lim_n":[16],"a(n,i)$.":[17],"Aldous":[18],"Janson":[20],"asked":[21],"whether":[22],"$\\sum_{i=2}^n":[23],"a(n,i)f(i)\\to\\sum_{i\\ge2}a(i)f(i)$":[24],"for":[25,49,62],"every":[26,50],"non-negative":[27],"$f$":[28,55],"of":[29,71,89,98],"polynomial":[30],"growth":[31],"with":[32,56,73],"a":[33,96],"finite":[34],"limit":[35],"sum,":[36],"Brandenberger,":[38],"Chin":[39],"Mossel":[41],"proved":[42],"this":[43],"when":[44],"$f(i)=O(i^{-\\varepsilon})$.":[45],"We":[46],"show":[47],"$\\delta>0$":[51],"there":[52],"is":[53,77],"an":[54],"$f(i)=O((\\log":[57],"i)^{-1+\\delta})$":[58],"$\\sum_i":[60],"a(i)f(i)<\\infty$":[61],"which":[63],"occupation":[65],"sums":[66],"are":[67],"unbounded,":[68],"along":[69],"values":[70],"$f(n)=0$.":[74],"The":[75],"cause":[76],"makes,":[84],"on":[85],"average,":[86],"least":[88],"order":[90],"$\\log":[91],"n/\\log\\log":[92],"n$":[93],"to":[95],"window":[97],"width":[99],"$n/(\\log":[100],"n)^2$":[101],"just":[102],"below":[103],"$n$.":[104]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
