{"id":"https://openalex.org/W3026795509","doi":"https://doi.org/10.1007/978-3-030-48006-6_9","title":"Convergence and Nonconvergence Laws for Random Expansions of Product Structures","display_name":"Convergence and Nonconvergence Laws for Random Expansions of Product Structures","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3026795509","doi":"https://doi.org/10.1007/978-3-030-48006-6_9","mag":"3026795509"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-48006-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-48006-6_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5080843415","display_name":"Anuj Dawar","orcid":"https://orcid.org/0000-0003-4014-8248"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Anuj Dawar","raw_affiliation_strings":["University of Cambridge, Cambridge, UK"],"affiliations":[{"raw_affiliation_string":"University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010064604","display_name":"Erich Gr\u00e4del","orcid":"https://orcid.org/0000-0002-8950-9991"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Erich Gr\u00e4del","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034213348","display_name":"Matthias Hoelzel","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Hoelzel","raw_affiliation_strings":["RWTH Aachen University, Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080843415"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.12552301,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"118","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9864000082015991,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7957853674888611},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5601046085357666},{"id":"https://openalex.org/keywords/law-of-large-numbers","display_name":"Law of large numbers","score":0.5434993505477905},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.4901512563228607},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.4548315703868866},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43428391218185425},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4197206497192383},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4164431691169739},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3676515817642212},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.23566484451293945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21292901039123535}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7957853674888611},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5601046085357666},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.5434993505477905},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.4901512563228607},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.4548315703868866},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43428391218185425},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4197206497192383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4164431691169739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3676515817642212},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.23566484451293945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21292901039123535},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-48006-6_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-48006-6_9","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W76753297","https://openalex.org/W139975798","https://openalex.org/W1026721552","https://openalex.org/W1482193060","https://openalex.org/W1985072883","https://openalex.org/W2034198367","https://openalex.org/W2063406522","https://openalex.org/W2085536555","https://openalex.org/W2726560500","https://openalex.org/W3149236991","https://openalex.org/W4234274921","https://openalex.org/W4252933876"],"related_works":["https://openalex.org/W2348480070","https://openalex.org/W4224286489","https://openalex.org/W4223985063","https://openalex.org/W4385379825","https://openalex.org/W1564609195","https://openalex.org/W1982128894","https://openalex.org/W1995753472","https://openalex.org/W2390957572","https://openalex.org/W2381670468","https://openalex.org/W2367503346"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}