{"id":"https://openalex.org/W7130409130","doi":"https://doi.org/10.48550/arxiv.2602.15585","title":"Optimal detection of planted stars via a random energy model","display_name":"Optimal detection of planted stars via a random energy model","publication_year":2026,"publication_date":"2026-02-17","ids":{"openalex":"https://openalex.org/W7130409130","doi":"https://doi.org/10.48550/arxiv.2602.15585"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2602.15585","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.15585","pdf_url":"https://arxiv.org/pdf/2602.15585","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.15585","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120614953","display_name":"Ijay Narang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Narang, Ijay","raw_affiliation_strings":["School of Computer Science , Georgia Institute of Technology ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science , Georgia Institute of Technology ,","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126279033","display_name":"Will Perkins","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Perkins, Will","raw_affiliation_strings":["School of Computer Science , Georgia Institute of Technology ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science , Georgia Institute of Technology ,","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048663183","display_name":"Timothy Wee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wee, Timothy L. H.","raw_affiliation_strings":["School of Mathematics , Georgia Institute of Technology ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , Georgia Institute of Technology ,","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.41940000653266907,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.41940000653266907,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.26339998841285706,"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/T11716","display_name":"Random Matrices and Applications","score":0.11230000108480453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/erdos-renyi-graphs","display_name":"Erd\u0151s-R\u00e9nyi random graphs","score":0.8759999871253967},{"id":"https://openalex.org/keywords/hypothesis-testing","display_name":"hypothesis testing","score":0.8920000195503235},{"id":"https://openalex.org/keywords/random-energy-model","display_name":"random energy model","score":0.9330000281333923},{"id":"https://openalex.org/keywords/spin-glass","display_name":"spin glass","score":0.6340000033378601},{"id":"https://openalex.org/keywords/condensation-phase-transition","display_name":"condensation phase transition","score":0.878000020980835},{"id":"https://openalex.org/keywords/total-variation-distance","display_name":"total variation distance","score":0.902999997138977},{"id":"https://openalex.org/keywords/sparse-graphs","display_name":"sparse graphs","score":0.3179999887943268}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6338000297546387},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6100999712944031},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.529699981212616},{"id":"https://openalex.org/C150846664","wikidata":"https://www.wikidata.org/wiki/Q7602306","display_name":"Stars","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41339999437332153},{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.3968999981880188},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C9483764","wikidata":"https://www.wikidata.org/wiki/Q585740","display_name":"Likelihood-ratio test","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.34360000491142273},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3246999979019165},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3077000081539154},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2964000105857849},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29600000381469727},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27889999747276306},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C36382193","wikidata":"https://www.wikidata.org/wiki/Q7068966","display_name":"Null model","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2602.15585","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.15585","pdf_url":"https://arxiv.org/pdf/2602.15585","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":"doi:10.48550/arxiv.2602.15585","doi":"https://doi.org/10.48550/arxiv.2602.15585","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.15585","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2602.15585","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.15585","pdf_url":"https://arxiv.org/pdf/2602.15585","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5281999466","display_name":"Collaborative Research: AF: Small: Sampling and Optimization under Global Constraints","funder_award_id":"2309708","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7130409130.pdf","grobid_xml":"https://content.openalex.org/works/W7130409130.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4417474160","https://openalex.org/W4413408106","https://openalex.org/W3141135580","https://openalex.org/W1977302966","https://openalex.org/W4391060399","https://openalex.org/W6891873255","https://openalex.org/W7164907207","https://openalex.org/W4221145812","https://openalex.org/W4364320961","https://openalex.org/W4407571036"],"abstract_inverted_index":{"We":[0,20],"study":[1],"the":[2,10,22,33,38,44,53,56,65,73],"problem":[3],"of":[4,32,55,72],"detecting":[5],"a":[6,17,60],"planted":[7],"star":[8,34],"in":[9,28,30,49,64],"Erd{\u0151}s--R{\u00e9}nyi":[11],"random":[12,74],"graph":[13],"$G(n,m)$,":[14],"formulated":[15],"as":[16],"hypothesis":[18],"test.":[19],"determine":[21],"scaling":[23],"window":[24],"for":[25],"critical":[26],"detection":[27],"$m$":[29],"terms":[31],"size,":[35],"and":[36,46],"characterize":[37],"asymptotic":[39],"total":[40],"variation":[41],"distance":[42],"between":[43],"null":[45],"alternative":[47],"hypotheses":[48],"this":[50],"window.":[51],"In":[52],"course":[54],"proofs":[57],"we":[58],"show":[59],"condensation":[61],"phase":[62],"transition":[63],"likelihood":[66],"ratio":[67],"that":[68,71],"closely":[69],"resembles":[70],"energy":[75],"model":[76],"from":[77],"spin":[78],"glass":[79],"theory.":[80]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-02-19T00:00:00"}