{"id":"https://openalex.org/W2999130160","doi":"https://doi.org/10.1137/19m1265314","title":"Invariant Measures for Integrable Spin Chains and an Integrable Discrete Nonlinear Schr\u00f6dinger Equation","display_name":"Invariant Measures for Integrable Spin Chains and an Integrable Discrete Nonlinear Schr\u00f6dinger Equation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2999130160","doi":"https://doi.org/10.1137/19m1265314","mag":"2999130160"},"language":"en","primary_location":{"id":"doi:10.1137/19m1265314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1265314","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","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/A5082831968","display_name":"Yannis Angelopoulos","orcid":"https://orcid.org/0000-0002-1997-3326"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yannis Angelopoulos","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060648196","display_name":"Rowan Killip","orcid":"https://orcid.org/0000-0002-4272-7916"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rowan Killip","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5091485408","display_name":"Monica Vi\u015fan","orcid":"https://orcid.org/0009-0001-8987-3187"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Monica Visan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5082831968"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7895,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63910061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"52","issue":"1","first_page":"135","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9995999932289124,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9995999932289124,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9983999729156494,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.8950272798538208},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7453891038894653},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7196124792098999},{"id":"https://openalex.org/keywords/gibbs-measure","display_name":"Gibbs measure","score":0.6072026491165161},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5693001747131348},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.46331122517585754},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.4560045003890991},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4432113766670227},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.42417067289352417},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.41153138875961304},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.40900319814682007},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3273965120315552},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16926690936088562},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12857425212860107}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.8950272798538208},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7453891038894653},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7196124792098999},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.6072026491165161},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5693001747131348},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.46331122517585754},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.4560045003890991},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4432113766670227},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.42417067289352417},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.41153138875961304},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40900319814682007},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3273965120315552},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16926690936088562},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12857425212860107},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1265314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1265314","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G5403869712","display_name":null,"funder_award_id":"DMS-1500707","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7292735915","display_name":null,"funder_award_id":"DMS-1600942","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1965612019","https://openalex.org/W1983444175","https://openalex.org/W1984287771","https://openalex.org/W1989438412","https://openalex.org/W1993671632","https://openalex.org/W1994687600","https://openalex.org/W2020462487","https://openalex.org/W2033689810","https://openalex.org/W2044503648","https://openalex.org/W2059955848","https://openalex.org/W2072950705","https://openalex.org/W2080784173","https://openalex.org/W2087237315","https://openalex.org/W2093785095","https://openalex.org/W2094983924","https://openalex.org/W2107971449","https://openalex.org/W2108797614","https://openalex.org/W2112324306","https://openalex.org/W2118551292","https://openalex.org/W2132353975","https://openalex.org/W2157662523","https://openalex.org/W2227235496","https://openalex.org/W2271789368","https://openalex.org/W2809537538","https://openalex.org/W2962874417","https://openalex.org/W2963080232","https://openalex.org/W2963864581","https://openalex.org/W2963967918","https://openalex.org/W3098254535","https://openalex.org/W4235322506","https://openalex.org/W4300015443"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W2044787408","https://openalex.org/W4289551052","https://openalex.org/W4249228129","https://openalex.org/W4390756076"],"abstract_inverted_index":{"We":[0,72,158],"consider":[1,73],"discrete":[2,69,153,171],"analogues":[3],"of":[4,18,31,87,107,135,143,155,164],"two":[5,180],"well-known":[6],"open":[7],"problems":[8],"regarding":[9],"invariant":[10],"measures":[11],"for":[12,22,82,109],"dispersive":[13],"PDE,":[14],"namely,":[15],"the":[16,19,23,29,49,77,88,103,124,133,136,151,165,170,179],"invariance":[17,30,142],"Gibbs":[20,114,125],"measure":[21,126,145],"continuum":[24,41],"(classical)":[25],"Heisenberg":[26,90],"model":[27,93],"and":[28,46,64,99,105,121],"white":[32,156],"noise":[33],"under":[34,129],"focusing":[35,137],"cubic":[36],"nonlinear":[37],"Schr\u00f6dinger":[38],"equation.":[39],"These":[40],"models":[42,75,181],"are":[43,60],"completely":[44,62,84],"integrable":[45,63,85],"connected":[47,66],"by":[48,67,96,175],"Hasimoto":[50,70,172],"transform;":[51],"correspondingly,":[52],"we":[53,101,117,140,147],"focus":[54],"our":[55],"attention":[56],"on":[57,76],"discretizations":[58],"that":[59,123,146,177],"also":[61,65,159],"a":[68,83,113,144,161],"transform.":[71],"these":[74,130],"infinite":[78],"lattice":[79],"${\\mathbb{Z}}$.":[80],"Concretely,":[81],"variant":[86],"classical":[89],"spin":[91],"chain":[92],"(introduced":[94],"independently":[95],"Haldane,":[97],"Ishimori,":[98],"Sklyanin)":[100],"prove":[102,141],"existence":[104],"uniqueness":[106],"solutions":[108],"initial":[110],"data":[111],"following":[112],"law":[115],"(which":[116],"show":[118,122,149],"is":[119,127,150],"unique)":[120],"preserved":[128],"dynamics.":[131],"In":[132],"setting":[134],"Ablowitz--Ladik":[138],"system,":[139],"will":[148],"appropriate":[152],"analogue":[154],"noise.":[157],"include":[160],"thorough":[162],"discussion":[163],"Poisson":[166],"geometry":[167],"associated":[168],"to":[169],"transform":[173],"introduced":[174],"Ishimori":[176],"connects":[178],"studied":[182],"in":[183],"this":[184],"article.":[185]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
