{"id":"https://openalex.org/W2135153977","doi":"https://doi.org/10.37236/424","title":"Rotor-Router Aggregation on the Layered Square Lattice","display_name":"Rotor-Router Aggregation on the Layered Square Lattice","publication_year":2010,"publication_date":"2010-11-05","ids":{"openalex":"https://openalex.org/W2135153977","doi":"https://doi.org/10.37236/424","mag":"2135153977"},"language":"en","primary_location":{"id":"doi:10.37236/424","is_oa":true,"landing_page_url":"https://doi.org/10.37236/424","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r152/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r152/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003227426","display_name":"Wouter Kager","orcid":"https://orcid.org/0000-0002-3400-6158"},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Wouter Kager","raw_affiliation_strings":["Vrije Universiteit Amsterdam ,"],"affiliations":[{"raw_affiliation_string":"Vrije Universiteit Amsterdam ,","institution_ids":["https://openalex.org/I865915315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052050258","display_name":"Lionel Levine","orcid":"https://orcid.org/0000-0003-0105-6754"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lionel Levine","raw_affiliation_strings":["Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003227426"],"corresponding_institution_ids":["https://openalex.org/I865915315"],"apc_list":null,"apc_paid":null,"fwci":2.386,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.87962005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9998999834060669,"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":0.9998999834060669,"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/T11716","display_name":"Random Matrices and Applications","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.8052729368209839},{"id":"https://openalex.org/keywords/square-lattice","display_name":"Square lattice","score":0.7679832577705383},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6519458293914795},{"id":"https://openalex.org/keywords/router","display_name":"Router","score":0.6299657821655273},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.627531111240387},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5645057559013367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5493745803833008},{"id":"https://openalex.org/keywords/diamond","display_name":"Diamond","score":0.5490931272506714},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.5071771144866943},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4926026463508606},{"id":"https://openalex.org/keywords/hexagonal-lattice","display_name":"Hexagonal lattice","score":0.458426833152771},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.44888582825660706},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3689184784889221},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32939428091049194},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30438607931137085},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.2853478491306305},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18206268548965454},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.1527264416217804},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.09840857982635498},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.08889168500900269},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07497149705886841},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06369301676750183}],"concepts":[{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.8052729368209839},{"id":"https://openalex.org/C2777620828","wikidata":"https://www.wikidata.org/wiki/Q7582067","display_name":"Square lattice","level":3,"score":0.7679832577705383},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6519458293914795},{"id":"https://openalex.org/C2775896111","wikidata":"https://www.wikidata.org/wiki/Q642560","display_name":"Router","level":2,"score":0.6299657821655273},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.627531111240387},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5645057559013367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5493745803833008},{"id":"https://openalex.org/C2776921476","wikidata":"https://www.wikidata.org/wiki/Q5283","display_name":"Diamond","level":2,"score":0.5490931272506714},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5071771144866943},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4926026463508606},{"id":"https://openalex.org/C90626534","wikidata":"https://www.wikidata.org/wiki/Q4523381","display_name":"Hexagonal lattice","level":3,"score":0.458426833152771},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.44888582825660706},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3689184784889221},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32939428091049194},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30438607931137085},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.2853478491306305},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18206268548965454},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.1527264416217804},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.09840857982635498},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.08889168500900269},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07497149705886841},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06369301676750183},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/424","is_oa":true,"landing_page_url":"https://doi.org/10.37236/424","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r152/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/424","is_oa":true,"landing_page_url":"https://doi.org/10.37236/424","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r152/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2135153977.pdf","grobid_xml":"https://content.openalex.org/works/W2135153977.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1511301024","https://openalex.org/W2006397962","https://openalex.org/W2018777507","https://openalex.org/W2024766920","https://openalex.org/W2061960942","https://openalex.org/W2102663108","https://openalex.org/W2111084941","https://openalex.org/W2113295388","https://openalex.org/W2121114289","https://openalex.org/W2144828388","https://openalex.org/W2156705116","https://openalex.org/W2167628842","https://openalex.org/W2950816065","https://openalex.org/W3038123220","https://openalex.org/W3098102571","https://openalex.org/W4242437876","https://openalex.org/W6630220140","https://openalex.org/W6654968535","https://openalex.org/W6656893828"],"related_works":["https://openalex.org/W2087433219","https://openalex.org/W2105466040","https://openalex.org/W1977023273","https://openalex.org/W2023363113","https://openalex.org/W1983780373","https://openalex.org/W2142528991","https://openalex.org/W2338427186","https://openalex.org/W2074487964","https://openalex.org/W1975917416","https://openalex.org/W2896254755"],"abstract_inverted_index":{"In":[0],"rotor-router":[1],"aggregation":[2],"on":[3,47],"the":[4,11,28,42,48,75],"square":[5],"lattice":[6],"$\\mathbb{Z}^2$,":[7],"particles":[8],"starting":[9],"at":[10],"origin":[12],"perform":[13],"deterministic":[14],"analogues":[15],"of":[16,27,30,62,72],"random":[17],"walks":[18],"until":[19],"reaching":[20],"an":[21],"unoccupied":[22],"site.":[23],"The":[24],"limiting":[25,55],"shape":[26,56],"cluster":[29,77],"occupied":[31,76],"sites":[32,46],"is":[33,58],"a":[34,38,54,59,63,69,80],"disk.":[35,64],"We":[36,65],"consider":[37],"small":[39],"change":[40],"to":[41],"routing":[43],"mechanism":[44],"for":[45,68],"$x$-":[49],"and":[50],"$y$-axes,":[51],"resulting":[52],"in":[53],"which":[57],"diamond":[60],"instead":[61],"show":[66],"that":[67],"certain":[70],"choice":[71],"initial":[73],"rotors,":[74],"grows":[78],"as":[79],"perfect":[81],"diamond.":[82]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}