{"id":"https://openalex.org/W4414708837","doi":"https://doi.org/10.1017/jpr.2025.10030","title":"Limit theorems for the number of crossings and stress in projections of a random geometric graph","display_name":"Limit theorems for the number of crossings and stress in projections of a random geometric graph","publication_year":2025,"publication_date":"2025-10-01","ids":{"openalex":"https://openalex.org/W4414708837","doi":"https://doi.org/10.1017/jpr.2025.10030"},"language":"en","primary_location":{"id":"doi:10.1017/jpr.2025.10030","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10030","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1017/jpr.2025.10030","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091872975","display_name":"Hanna D\u00f6ring","orcid":null},"institutions":[{"id":"https://openalex.org/I170658231","display_name":"Osnabr\u00fcck University","ror":"https://ror.org/04qmmjx98","country_code":"DE","type":"education","lineage":["https://openalex.org/I170658231"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hanna D\u00f6ring","raw_affiliation_strings":["Osnabr\u00fcck University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Osnabr\u00fcck University","institution_ids":["https://openalex.org/I170658231"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5115913041","display_name":"Lianne de Jonge","orcid":null},"institutions":[{"id":"https://openalex.org/I170658231","display_name":"Osnabr\u00fcck University","ror":"https://ror.org/04qmmjx98","country_code":"DE","type":"education","lineage":["https://openalex.org/I170658231"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lianne De Jonge","raw_affiliation_strings":["Osnabr\u00fcck University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Osnabr\u00fcck University","institution_ids":["https://openalex.org/I170658231"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I170658231"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35746212,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"1","first_page":"258","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.991599977016449,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.6317999958992004},{"id":"https://openalex.org/keywords/point-process","display_name":"Point process","score":0.555400013923645},{"id":"https://openalex.org/keywords/geometric-graph-theory","display_name":"Geometric graph theory","score":0.524399995803833},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5128999948501587},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.4803999960422516},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.46939998865127563},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"Central limit theorem","score":0.44749999046325684},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4408000111579895},{"id":"https://openalex.org/keywords/spatial-network","display_name":"Spatial network","score":0.4390000104904175},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4251999855041504}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9064000248908997},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.6317999958992004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5827000141143799},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C173547177","wikidata":"https://www.wikidata.org/wiki/Q1503271","display_name":"Geometric graph theory","level":5,"score":0.524399995803833},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5128999948501587},{"id":"https://openalex.org/C16757284","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson point process","level":3,"score":0.4803999960422516},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.46939998865127563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46720001101493835},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.44749999046325684},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C53471067","wikidata":"https://www.wikidata.org/wiki/Q7574076","display_name":"Spatial network","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4251999855041504},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.37599998712539673},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.36550000309944153},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C7605037","wikidata":"https://www.wikidata.org/wiki/Q327164","display_name":"Geometric probability","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.2935999929904938},{"id":"https://openalex.org/C52627884","wikidata":"https://www.wikidata.org/wiki/Q4424101","display_name":"Random compact set","level":4,"score":0.28529998660087585},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2825999855995178},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.26829999685287476},{"id":"https://openalex.org/C166144826","wikidata":"https://www.wikidata.org/wiki/Q1145117","display_name":"Poisson process","level":3,"score":0.26409998536109924},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/jpr.2025.10030","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10030","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/jpr.2025.10030","is_oa":true,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10030","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W630423399","https://openalex.org/W1535274625","https://openalex.org/W1560672772","https://openalex.org/W1633817406","https://openalex.org/W1984830753","https://openalex.org/W2020340581","https://openalex.org/W2028534697","https://openalex.org/W2060205664","https://openalex.org/W2078972733","https://openalex.org/W2767091268","https://openalex.org/W2888463608","https://openalex.org/W2937270620","https://openalex.org/W2951800124","https://openalex.org/W2963234650","https://openalex.org/W2986610185","https://openalex.org/W3097990213","https://openalex.org/W4385651993"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,46,75],"consider":[2],"the":[3,40,50,72,84,93,98,103],"number":[4,52,85],"of":[5,36,42,53,86],"edge":[6],"crossings":[7,38,54,87],"in":[8,71,102],"a":[9,16,32,43,57,67,78,89,109],"random":[10,17,104],"graph":[11,19,106],"drawing":[12],"generated":[13],"by":[14],"projecting":[15],"geometric":[18,105],"on":[20],"some":[21],"compact":[22],"convex":[23],"set":[24],"$W\\subset":[25],"\\mathbb{R}^d$":[26],",":[27,30],"$d\\geq":[28],"3$":[29],"onto":[31],"plane.":[33],"The":[34],"positions":[35],"these":[37],"form":[39],"support":[41],"point":[44,63,69],"process.":[45],"show":[47,77],"that":[48,95],"if":[49],"expected":[51,99],"converges":[55,65,107],"to":[56,66,108],"positive":[58,110],"but":[59],"finite":[60,111],"value,":[61],"this":[62],"process":[64,70],"Poisson":[68],"Kantorovich\u2013Rubinstein":[73],"distance.":[74],"further":[76],"multivariate":[79],"central":[80],"limit":[81],"theorem":[82],"between":[83],"and":[88],"second":[90],"variable":[91],"called":[92],"stress":[94],"holds":[96],"when":[97],"vertex":[100],"degree":[101],"value.":[112]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}