{"id":"https://openalex.org/W4415795166","doi":"https://doi.org/10.1017/jpr.2025.10035","title":"Poisson approximation for cycles in the generalised random graph","display_name":"Poisson approximation for cycles in the generalised random graph","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415795166","doi":"https://doi.org/10.1017/jpr.2025.10035"},"language":"en","primary_location":{"id":"doi:10.1017/jpr.2025.10035","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10035","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093393102","display_name":"Matthias Lienau","orcid":"https://orcid.org/0009-0000-7269-3342"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]},{"id":"https://openalex.org/I884043246","display_name":"Hamburg University of Technology","ror":"https://ror.org/04bs1pb34","country_code":"DE","type":"education","lineage":["https://openalex.org/I884043246"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Lienau","raw_affiliation_strings":["Hamburg University of Technology"],"raw_orcid":"https://orcid.org/0009-0000-7269-3342","affiliations":[{"raw_affiliation_string":"Hamburg University of Technology","institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5093393102"],"corresponding_institution_ids":["https://openalex.org/I159176309","https://openalex.org/I884043246"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27260835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"1","first_page":"433","last_page":"457"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.4562000036239624,"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/T11716","display_name":"Random Matrices and Applications","score":0.4562000036239624,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.12929999828338623,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11720","display_name":"Probability and Risk Models","score":0.08190000057220459,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5511999726295471},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5458999872207642},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.5181999802589417},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5038999915122986},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.4925999939441681},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.43380001187324524},{"id":"https://openalex.org/keywords/poisson-process","display_name":"Poisson process","score":0.4113999903202057},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.3968000113964081},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.39010000228881836}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9211000204086304},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.605400025844574},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5511999726295471},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5458999872207642},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5038999915122986},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.4925999939441681},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4666000008583069},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.4113999903202057},{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.3968000113964081},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.39010000228881836},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3889999985694885},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C177255742","wikidata":"https://www.wikidata.org/wiki/Q4109953","display_name":"Branching process","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.33390000462532043},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.31290000677108765},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.30660000443458557},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C19332903","wikidata":"https://www.wikidata.org/wiki/Q7623247","display_name":"Strength of a graph","level":5,"score":0.28459998965263367},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26579999923706055},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/jpr.2025.10035","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10035","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W390146837","https://openalex.org/W1988529767","https://openalex.org/W2016966047","https://openalex.org/W2017170340","https://openalex.org/W2027377866","https://openalex.org/W2057505998","https://openalex.org/W2083750870","https://openalex.org/W2115976335","https://openalex.org/W2122635167","https://openalex.org/W2128097224","https://openalex.org/W2154608741","https://openalex.org/W2167595480","https://openalex.org/W2506550686","https://openalex.org/W2605906613","https://openalex.org/W2614668157","https://openalex.org/W2899923712","https://openalex.org/W2903647410","https://openalex.org/W2949935167","https://openalex.org/W2950850272","https://openalex.org/W2975374143","https://openalex.org/W3006443489","https://openalex.org/W3082642148","https://openalex.org/W3146341627","https://openalex.org/W3207353010","https://openalex.org/W4214601773"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"The":[1,12],"generalised":[2],"random":[3],"graph":[4,103,141],"contains":[5],"n":[6],"vertices":[7,20],"with":[8],"positive":[9],"i.i.d.":[10],"weights.":[11,25],"probability":[13],"of":[14,50,62,73,99,117,121,130,133,146],"adding":[15],"an":[16],"edge":[17],"between":[18],"two":[19],"is":[21,87,104,142],"increasing":[22],"in":[23,56],"their":[24],"We":[26,59],"require":[27],"the":[28,38,51,57,70,74,82,102,115,127,131,134,140,154,158],"weight":[29],"distribution":[30,129],"to":[31,64,110,153],"have":[32],"finite":[33,77],"second":[34],"moments,":[35],"and":[36,136,157],"study":[37],"point":[39,67],"process":[40],"$\\mathcal{C}_n$":[41,63,86],"on":[42,89],"$\\{3,4,\\ldots\\}$":[43],",":[44,94],"which":[45],"counts":[46],"how":[47],"many":[48],"cycles":[49,138],"respective":[52],"length":[53,132],"are":[54],"present":[55],"graph.":[58],"establish":[60],"convergence":[61],"a":[65,90,97,118],"Poisson":[66],"process.":[68],"Under":[69],"stronger":[71],"assumption":[72],"weights":[75],"having":[76],"fourth":[78],"moments":[79],"we":[80,95,107,125],"provide":[81,96],"following":[83],"results.":[84],"When":[85],"evaluated":[88],"bounded":[91],"set":[92],"A":[93,113],"rate":[98,120],"convergence.":[100,122,147],"If":[101],"additionally":[105],"subcritical,":[106,143],"extend":[108],"this":[109,124],"unbounded":[111],"sets":[112],"at":[114],"cost":[116],"slower":[119],"From":[123],"deduce":[126],"limiting":[128],"shortest":[135],"longest":[137],"when":[139],"including":[144],"rates":[145],"All":[148],"mentioned":[149],"results":[150],"also":[151],"apply":[152],"Chung\u2013Lu":[155],"model":[156],"Norros\u2013Reittu":[159],"model.":[160]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-11-03T00:00:00"}