{"id":"https://openalex.org/W4398244505","doi":"https://doi.org/10.1017/s0963548324000129","title":"Noise sensitivity of the minimum spanning tree of the complete graph","display_name":"Noise sensitivity of the minimum spanning tree of the complete graph","publication_year":2024,"publication_date":"2024-05-23","ids":{"openalex":"https://openalex.org/W4398244505","doi":"https://doi.org/10.1017/s0963548324000129"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548324000129","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548324000129","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/80A070E812DC451FE7DADAFB87FAC54B/S0963548324000129a.pdf/div-class-title-noise-sensitivity-of-the-minimum-spanning-tree-of-the-complete-graph-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"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":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/80A070E812DC451FE7DADAFB87FAC54B/S0963548324000129a.pdf/div-class-title-noise-sensitivity-of-the-minimum-spanning-tree-of-the-complete-graph-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092171879","display_name":"Omer Israeli","orcid":null},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Omer Israeli","raw_affiliation_strings":["Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052520151","display_name":"Yuval Peled","orcid":"https://orcid.org/0000-0003-1516-1918"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yuval Peled","raw_affiliation_strings":["Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel"],"raw_orcid":"https://orcid.org/0000-0003-1516-1918","affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052520151"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13322771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"6","first_page":"708","last_page":"723"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9965000152587891,"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/T11476","display_name":"Graph theory and applications","score":0.9965000152587891,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9793999791145325,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T13234","display_name":"advanced mathematical theories","score":0.9767000079154968,"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/spanning-tree","display_name":"Spanning tree","score":0.6500545144081116},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5009500980377197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4397865831851959},{"id":"https://openalex.org/keywords/minimum-spanning-tree","display_name":"Minimum spanning tree","score":0.4303268790245056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3673378825187683},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3143923282623291},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2727583050727844},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.15366610884666443},{"id":"https://openalex.org/keywords/electronic-engineering","display_name":"Electronic engineering","score":0.08224207162857056}],"concepts":[{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.6500545144081116},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5009500980377197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4397865831851959},{"id":"https://openalex.org/C13743678","wikidata":"https://www.wikidata.org/wiki/Q240464","display_name":"Minimum spanning tree","level":2,"score":0.4303268790245056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3673378825187683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3143923282623291},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2727583050727844},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.15366610884666443},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.08224207162857056}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548324000129","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548324000129","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/80A070E812DC451FE7DADAFB87FAC54B/S0963548324000129a.pdf/div-class-title-noise-sensitivity-of-the-minimum-spanning-tree-of-the-complete-graph-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"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":"Combinatorics, Probability and Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0963548324000129","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548324000129","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/80A070E812DC451FE7DADAFB87FAC54B/S0963548324000129a.pdf/div-class-title-noise-sensitivity-of-the-minimum-spanning-tree-of-the-complete-graph-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"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":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4398244505.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1590619386","https://openalex.org/W1965680834","https://openalex.org/W2003914969","https://openalex.org/W2012184276","https://openalex.org/W2027442384","https://openalex.org/W2054812794","https://openalex.org/W2056513564","https://openalex.org/W2071346873","https://openalex.org/W2133263321","https://openalex.org/W2152880689","https://openalex.org/W2161066177","https://openalex.org/W2168790747","https://openalex.org/W2802739963","https://openalex.org/W2949874440","https://openalex.org/W2962759144","https://openalex.org/W2962953861","https://openalex.org/W3082144842","https://openalex.org/W3098764148","https://openalex.org/W3121646137","https://openalex.org/W4233869717","https://openalex.org/W4392292651","https://openalex.org/W6966805651"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2099915933","https://openalex.org/W2418231958","https://openalex.org/W4380840098","https://openalex.org/W3116169590","https://openalex.org/W1703428550","https://openalex.org/W2044443696","https://openalex.org/W3101281637","https://openalex.org/W2390742649","https://openalex.org/W1561849181"],"abstract_inverted_index":{"Abstract":[0],"We":[1,54],"study":[2],"the":[3,7,13,30,44,50,58,73,84,100,104,114,123,132,142,146,162],"noise":[4,85,115,136],"sensitivity":[5,116],"of":[6,12,60,75,122,131,138,145,166],"minimum":[8,77,163],"spanning":[9,78,164],"tree":[10],"(MST)":[11],"$n$":[14],"-vertex":[15],"complete":[16],"graph":[17,31],"when":[18,29],"edges":[19],"are":[20,39],"assigned":[21],"independent":[22,91],"random":[23,92,133,148,168],"weights.":[24],"It":[25],"is":[26,33,63],"known":[27],"that":[28,56,125],"distance":[32,102],"rescaled":[34,76,105],"by":[35],"$n^{1/3}$":[36],"and":[37,82,117],"vertices":[38],"given":[40],"a":[41,128],"uniform":[42],"measure,":[43],"MST":[45,124],"converges":[46,87],"in":[47,49,88,110],"distribution":[48,89],"Gromov\u2013Hausdorff\u2013Prokhorov":[51],"(GHP)":[52],"topology.":[53],"prove":[55,160],"if":[57,95],"weight":[59],"each":[61],"edge":[62],"resampled":[64],"independently":[65],"with":[66,141],"probability":[67],"$\\varepsilon":[68,96],"\\gg":[69],"n^{-1/3}$":[70,98],",":[71,99],"then":[72],"pair":[74],"trees":[79,106],"\u2013":[80,86],"before":[81],"after":[83],"to":[90,108,127],"spaces.":[93],"Conversely,":[94],"\\ll":[97],"GHP":[101],"between":[103],"goes":[107],"$0$":[109],"probability.":[111],"This":[112],"implies":[113],"stability":[118],"for":[119],"every":[120],"property":[121],"corresponds":[126],"continuity":[129],"set":[130],"limit.":[134],"The":[135],"threshold":[137],"$n^{-1/3}$":[139],"coincides":[140],"critical":[143,167],"window":[144],"Erd\u0151s-R\u00e9nyi":[147],"graphs.":[149,169],"In":[150],"fact,":[151],"these":[152],"results":[153],"follow":[154],"from":[155],"an":[156],"analog":[157],"theorem":[158],"we":[159],"regarding":[161],"forest":[165]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}