{"id":"https://openalex.org/W7220903695","doi":"https://doi.org/10.48550/arxiv.2610.08149","title":"Infinite-mean Galton-Watson trees have zero random-interchange threshold","display_name":"Infinite-mean Galton-Watson trees have zero random-interchange threshold","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220903695","doi":"https://doi.org/10.48550/arxiv.2610.08149"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08149","pdf_url":"https://arxiv.org/pdf/2610.08149","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08149","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106276620","display_name":"Andreas Klippel","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klippel, Andreas","raw_affiliation_strings":["\u2017 Johannes Gutenberg University Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u2017 Johannes Gutenberg University Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150375907","display_name":"Benjamin Lees","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lees, Benjamin","raw_affiliation_strings":["School of Mathematics , University of Leeds , Leeds , LS2 9JT , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , University of Leeds , Leeds , LS2 9JT , UK","institution_ids":["https://openalex.org/I130828816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036022828","display_name":"Christian M\u00f6nch","orcid":"https://orcid.org/0000-0002-6531-6482","observed_orcids":["https://orcid.org/0000-0002-6531-6482"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M\u00f6nch, Christian","raw_affiliation_strings":["Independent Researcher , 64289 Darmstadt , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher , 64289 Darmstadt , Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9984999895095825,"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":0.9984999895095825,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":9.999999747378752e-05,"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/galton-watson-trees","display_name":"Galton-Watson trees","score":0.9259999990463257},{"id":"https://openalex.org/keywords/critical-parameters","display_name":"critical parameters","score":0.5759999752044678},{"id":"https://openalex.org/keywords/random-permutations","display_name":"random permutations","score":0.4050000011920929},{"id":"https://openalex.org/keywords/random-surfaces","display_name":"random surfaces","score":0.902999997138977},{"id":"https://openalex.org/keywords/locally-finite-graphs","display_name":"locally finite graphs","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8439000248908997},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6256999969482422},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5788999795913696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.539900004863739},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.525600016117096},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.521399974822998},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4778999984264374},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.40220001339912415},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.3596999943256378},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C112672928","wikidata":"https://www.wikidata.org/wiki/Q239526","display_name":"Offspring","level":3,"score":0.31610000133514404},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.25049999356269836},{"id":"https://openalex.org/C37727645","wikidata":"https://www.wikidata.org/wiki/Q6675770","display_name":"Loop-erased random walk","level":4,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08149","pdf_url":"https://arxiv.org/pdf/2610.08149","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.08149","doi":"https://doi.org/10.48550/arxiv.2610.08149","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08149","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08149","pdf_url":"https://arxiv.org/pdf/2610.08149","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,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220903695.pdf","grobid_xml":"https://content.openalex.org/works/W7220903695.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W205074548","https://openalex.org/W1991020635","https://openalex.org/W1991748622","https://openalex.org/W1995804065","https://openalex.org/W2036002806","https://openalex.org/W2039394743","https://openalex.org/W2796132585","https://openalex.org/W2911983703","https://openalex.org/W2952866184","https://openalex.org/W2986376061","https://openalex.org/W3128575911","https://openalex.org/W4310560895","https://openalex.org/W4401307502","https://openalex.org/W4415336993"],"related_works":["https://openalex.org/W1981147534","https://openalex.org/W4415336993","https://openalex.org/W2806406298","https://openalex.org/W4399593550","https://openalex.org/W2951688377","https://openalex.org/W7100759831","https://openalex.org/W7096716517","https://openalex.org/W4400542094","https://openalex.org/W1970621027","https://openalex.org/W2937221887"],"abstract_inverted_index":{"We":[0],"prove":[1],"that,":[2],"on":[3,28],"a":[4,41,72],"Galton-Watson":[5,46],"tree":[6,69],"with":[7,31,48],"almost":[8],"surely":[9],"finite":[10,45,73],"offspring":[11,14,49],"and":[12,55],"infinite":[13,25],"mean,":[15],"the":[16,32,53,62,68],"random":[17,81],"interchange":[18],"process":[19],"has":[20],"critical":[21,57],"parameter":[22],"zero":[23],"for":[24,43,80],"cycles,":[26],"conditionally":[27],"survival.":[29],"Combined":[30],"finite-mean":[33],"strict":[34],"inequality":[35],"established":[36],"in":[37,51,61],"\\emph{arXiv:2503.03319},":[38],"this":[39],"gives":[40],"dichotomy":[42],"locally":[44],"trees":[47],"mean":[50],"$(1,\\infty]$:":[52],"loop":[54],"link":[56],"parameters":[58],"coincide":[59],"exactly":[60],"infinite-mean":[63],"case.":[64],"The":[65],"proof":[66],"reduces":[67],"problem":[70],"to":[71],"permutation":[74],"estimate":[75],"derived":[76],"from":[77],"peeling":[78],"estimates":[79],"surfaces.":[82]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}