{"id":"https://openalex.org/W7225654604","doi":"https://doi.org/10.5281/zenodo.24069900","title":"A tree automaton with infinitely many rogue fixed points under every supercritical offspring law","display_name":"A tree automaton with infinitely many rogue fixed points under every supercritical offspring law","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225654604","doi":"https://doi.org/10.5281/zenodo.24069900"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24069900","doi":"https://doi.org/10.5281/zenodo.24069900","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069900","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.24069900","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":0.6898999810218811,"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":0.6898999810218811,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.1662999987602234,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.10000000149011612,"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/tree-automata","display_name":"tree automata","score":0.9649999737739563},{"id":"https://openalex.org/keywords/fixed-points","display_name":"fixed points","score":0.8830000162124634},{"id":"https://openalex.org/keywords/binary-branching","display_name":"binary branching","score":0.722000002861023},{"id":"https://openalex.org/keywords/quadratic-stochastic-operators","display_name":"quadratic stochastic operators","score":0.902999997138977},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.4390000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465000152587891},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5461999773979187},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5202999711036682},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5059999823570251},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44440001249313354},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.3944999873638153},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35989999771118164},{"id":"https://openalex.org/C174784677","wikidata":"https://www.wikidata.org/wiki/Q176567","display_name":"Probabilistic automaton","level":3,"score":0.32120001316070557},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.31859999895095825},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C139423837","wikidata":"https://www.wikidata.org/wiki/Q243800","display_name":"Two-way deterministic finite automaton","level":5,"score":0.2775999903678894},{"id":"https://openalex.org/C2778583254","wikidata":"https://www.wikidata.org/wiki/Q2872598","display_name":"Tree automaton","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C165753454","wikidata":"https://www.wikidata.org/wiki/Q1020380","display_name":"B\u00fcchi automaton","level":4,"score":0.25760000944137573},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24069900","doi":"https://doi.org/10.5281/zenodo.24069900","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069900","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.24069901","doi":"https://doi.org/10.5281/zenodo.24069901","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069901","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.24069900","doi":"https://doi.org/10.5281/zenodo.24069900","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24069900","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/W4383604998","https://openalex.org/W2142707270","https://openalex.org/W145592316","https://openalex.org/W1587070528","https://openalex.org/W4415081348","https://openalex.org/W2093399617","https://openalex.org/W2047429950","https://openalex.org/W4206107158","https://openalex.org/W2018000427","https://openalex.org/W31764729"],"abstract_inverted_index":{"Johnson,":[0],"Podder":[1],"and":[2,43,84],"Skerman":[3],"asked":[4],"whether":[5],"a":[6,134],"tree":[7],"automaton":[8,25,69],"with":[9,33,80,94,116],"finitely":[10],"many,":[11],"but":[12],"at":[13],"least":[14],"three,":[15],"states":[16,35,72],"can":[17],"have":[18],"infinitely":[19],"many":[20],"fixed":[21,74],"points":[22,126],"of":[23,41,98,111],"its":[24],"distributional":[26],"map.":[27],"Under":[28],"binary":[29],"branching":[30],"an":[31,68,77],"example":[32],"three":[34],"is":[36,67,114],"implicit":[37],"in":[38],"earlier":[39],"work":[40],"Rozikov":[42],"Zada":[44],"on":[45,70,120],"quadratic":[46],"stochastic":[47],"operators.":[48],"We":[49],"show":[50],"that":[51,100],"the":[52,95,102,112,121,125,129],"phenomenon":[53],"holds":[54],"for":[55,76,124],"every":[56,64],"supercritical":[57],"offspring":[58,78,122],"law,":[59],"Poisson":[60],"laws":[61,99],"included.":[62],"For":[63],"$k\\ge2$":[65],"there":[66],"$k+1$":[71],"whose":[73],"points,":[75],"law":[79],"generating":[81],"function":[82],"$G$":[83],"mean":[85],"greater":[86],"than":[87,128],"one,":[88],"are":[89],"one":[90],"point":[91,110],"mass":[92,105],"together":[93],"$(k-1)$-dimensional":[96],"simplex":[97,113],"give":[101],"distinguished":[103],"state":[104],"$s_*$,":[106],"where":[107],"$G'(s_*)=1$.":[108],"Every":[109],"rogue,":[115],"no":[117],"moment":[118],"assumption":[119],"law;":[123],"other":[127],"$k$":[130],"vertices":[131],"this":[132],"has":[133],"short":[135],"self-contained":[136],"proof.":[137]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
