{"id":"https://openalex.org/W2921892452","doi":"https://doi.org/10.1214/19-aop1372","title":"The maximum of the four-dimensional membrane model","display_name":"The maximum of the four-dimensional membrane model","publication_year":2020,"publication_date":"2020-03-01","ids":{"openalex":"https://openalex.org/W2921892452","doi":"https://doi.org/10.1214/19-aop1372","mag":"2921892452"},"language":"en","primary_location":{"id":"doi:10.1214/19-aop1372","doi":"https://doi.org/10.1214/19-aop1372","is_oa":true,"landing_page_url":"https://doi.org/10.1214/19-aop1372","pdf_url":"https://projecteuclid.org/journals/annals-of-probability/volume-48/issue-2/The-maximum-of-the-four-dimensional-membrane-model/10.1214/19-AOP1372.pdf","source":{"id":"https://openalex.org/S40212770","display_name":"The Annals of Probability","issn_l":"0091-1798","issn":["0091-1798","2168-894X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Probability","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://projecteuclid.org/journals/annals-of-probability/volume-48/issue-2/The-maximum-of-the-four-dimensional-membrane-model/10.1214/19-AOP1372.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Florian Schweiger","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Florian Schweiger","raw_affiliation_strings":["Institut f\u00fcr angewandte Mathematik , Universit\u00e4t Bonn ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr angewandte Mathematik , Universit\u00e4t Bonn ,","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":3.0786,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.91704574,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"48","issue":"2","first_page":"714","last_page":"741"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.975600004196167,"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":0.975600004196167,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.005900000222027302,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0034000000450760126,"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/maximum-of-random-fields","display_name":"maximum of random fields","score":0.6700000166893005},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.7639999985694885},{"id":"https://openalex.org/keywords/green-s-function","display_name":"Green's function","score":0.6669999957084656},{"id":"https://openalex.org/keywords/finite-difference-schemes","display_name":"finite difference schemes","score":0.925000011920929},{"id":"https://openalex.org/keywords/approximation-error-estimates","display_name":"approximation error bounds","score":0.6769999861717224},{"id":"https://openalex.org/keywords/random-walks-on-graphs","display_name":"random walks on graphs","score":0.41600000858306885}],"concepts":[{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6159831285476685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6071143746376038},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5215449333190918},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49343958497047424},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4630826413631439},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.4383493661880493},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3608105480670929},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2972147464752197},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19441741704940796},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.10420215129852295},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0798606276512146},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1214/19-aop1372","doi":"https://doi.org/10.1214/19-aop1372","is_oa":true,"landing_page_url":"https://doi.org/10.1214/19-aop1372","pdf_url":"https://projecteuclid.org/journals/annals-of-probability/volume-48/issue-2/The-maximum-of-the-four-dimensional-membrane-model/10.1214/19-AOP1372.pdf","source":{"id":"https://openalex.org/S40212770","display_name":"The Annals of Probability","issn_l":"0091-1798","issn":["0091-1798","2168-894X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Probability","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1903.02522","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.02522","pdf_url":"https://arxiv.org/pdf/1903.02522","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":"mag:2921892452","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.02522.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CULeuclid:euclid.aop/1587542677","doi":null,"is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.aop/1587542677","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1903.02522","doi":"https://doi.org/10.48550/arxiv.1903.02522","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.02522","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1214/19-aop1372","doi":"https://doi.org/10.1214/19-aop1372","is_oa":true,"landing_page_url":"https://doi.org/10.1214/19-aop1372","pdf_url":"https://projecteuclid.org/journals/annals-of-probability/volume-48/issue-2/The-maximum-of-the-four-dimensional-membrane-model/10.1214/19-AOP1372.pdf","source":{"id":"https://openalex.org/S40212770","display_name":"The Annals of Probability","issn_l":"0091-1798","issn":["0091-1798","2168-894X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Probability","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1421283785","display_name":null,"funder_award_id":"Projekt-ID 390685813","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G3655066931","display_name":null,"funder_award_id":"GZ 2047/1","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G4274133347","display_name":null,"funder_award_id":"390685813","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"}],"funders":[{"id":"https://openalex.org/F4320322572","display_name":"Studienstiftung des Deutschen Volkes","ror":"https://ror.org/05xwwfy96"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2921892452.pdf","grobid_xml":"https://content.openalex.org/works/W2921892452.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1572521168","https://openalex.org/W1692060035","https://openalex.org/W1983529170","https://openalex.org/W1984642139","https://openalex.org/W2006282422","https://openalex.org/W2015955771","https://openalex.org/W2022385268","https://openalex.org/W2035865802","https://openalex.org/W2042669034","https://openalex.org/W2045148751","https://openalex.org/W2048900702","https://openalex.org/W2076567039","https://openalex.org/W2078535099","https://openalex.org/W2097649415","https://openalex.org/W2102318662","https://openalex.org/W2127600574","https://openalex.org/W2139310454","https://openalex.org/W2233386965","https://openalex.org/W2255272027","https://openalex.org/W2415276714","https://openalex.org/W2476525989","https://openalex.org/W2486406004","https://openalex.org/W2499078703","https://openalex.org/W2564506240","https://openalex.org/W2773006459","https://openalex.org/W2782743796","https://openalex.org/W2928270498","https://openalex.org/W2964063328","https://openalex.org/W3102870213","https://openalex.org/W4249877492"],"related_works":["https://openalex.org/W3018372592","https://openalex.org/W3100074738","https://openalex.org/W3105525756","https://openalex.org/W2950361872","https://openalex.org/W3001742344","https://openalex.org/W2469524243","https://openalex.org/W2952168204","https://openalex.org/W3016014818","https://openalex.org/W2949269633","https://openalex.org/W2197349688","https://openalex.org/W2951945106","https://openalex.org/W2895188618","https://openalex.org/W2733628767","https://openalex.org/W3129922248","https://openalex.org/W2338000073","https://openalex.org/W3014120224","https://openalex.org/W2962957329","https://openalex.org/W2087600519","https://openalex.org/W3199699850","https://openalex.org/W2498858925"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"the":[3,7,42,46,52,72,84,88],"centred":[4],"maximum":[5],"of":[6,14,27,45,55,62,75,87],"four-dimensional":[8],"membrane":[9],"model":[10],"on":[11],"a":[12,25],"box":[13],"sidelength":[15],"$N$":[16],"converges":[17],"in":[18],"distribution.":[19],"To":[20,65],"do":[21],"so,":[22],"we":[23,68],"use":[24,69],"criterion":[26],"Ding,":[28],"Roy":[29],"and":[30,37,58],"Zeitouni":[31],"(Ann.":[32],"Probab.":[33],"45":[34],"(2017)":[35],"3886\u20133928)":[36],"prove":[38],"sharp":[39],"estimates":[40,50,70],"for":[41,71,83],"Green\u2019s":[43,85],"function":[44,86],"discrete":[47],"Bilaplacian.":[48,90],"These":[49],"are":[51],"main":[53],"contribution":[54],"this":[56],"work":[57],"might":[59],"also":[60],"be":[61],"independent":[63],"interest.":[64],"derive":[66],"them,":[67],"approximation":[73],"quality":[74],"finite":[76],"difference":[77],"schemes":[78],"as":[79,81],"well":[80],"results":[82],"continuous":[89]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
