{"id":"https://openalex.org/W7214018737","doi":"https://doi.org/10.48550/arxiv.2609.22717","title":"Semiclassical reconstruction of the Toda pole lattice via analytic continuation of the Probabilistic Approach","display_name":"Semiclassical reconstruction of the Toda pole lattice via analytic continuation of the Probabilistic Approach","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214018737","doi":"https://doi.org/10.48550/arxiv.2609.22717"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.22717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22717","pdf_url":"https://arxiv.org/pdf/2609.22717","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/2609.22717","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054319884","display_name":"Jacques Distler B","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Distler, Jacques","raw_affiliation_strings":["Department of Physics , UT Austin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , UT Austin","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044827955","display_name":"Bahaa Elshimy","orcid":"https://orcid.org/0000-0002-8854-3346","observed_orcids":["https://orcid.org/0000-0002-8854-3346"]},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elshimy, Bahaa","raw_affiliation_strings":["Department of Physics , UT Austin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , UT Austin","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I86519309"],"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.586899995803833,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.586899995803833,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.3375999927520752,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.02199999988079071,"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/toda-field-theory","display_name":"Toda field theory","score":0.9950000047683716},{"id":"https://openalex.org/keywords/coulomb-gas-representation","display_name":"Coulomb gas representation","score":0.8019999861717224},{"id":"https://openalex.org/keywords/probabilistic-methods","display_name":"probabilistic methods","score":0.5429999828338623},{"id":"https://openalex.org/keywords/analytic-continuation","display_name":"analytic continuation","score":0.5329999923706055},{"id":"https://openalex.org/keywords/moment-problem","display_name":"moment problem","score":0.34299999475479126},{"id":"https://openalex.org/keywords/gaussian-measure","display_name":"Gaussian measure","score":0.7139999866485596},{"id":"https://openalex.org/keywords/mellin-barnes-representation","display_name":"Mellin-Barnes representation","score":0.8840000033378601},{"id":"https://openalex.org/keywords/semiclassical-limit","display_name":"semiclassical limit","score":0.6639999747276306},{"id":"https://openalex.org/keywords/lp-convergence","display_name":"Lp convergence","score":0.527999997138977}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.7685999870300293},{"id":"https://openalex.org/C7322696","wikidata":"https://www.wikidata.org/wiki/Q572090","display_name":"Toda lattice","level":3,"score":0.7684999704360962},{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.647599995136261},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.517300009727478},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.5092999935150146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5051000118255615},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.45649999380111694},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.44589999318122864},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.38359999656677246},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.3652999997138977},{"id":"https://openalex.org/C104416048","wikidata":"https://www.wikidata.org/wiki/Q302518","display_name":"Propagator","level":2,"score":0.3555999994277954},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3467999994754791},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3452000021934509},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3052999973297119},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29249998927116394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.28040000796318054},{"id":"https://openalex.org/C2778795013","wikidata":"https://www.wikidata.org/wiki/Q945127","display_name":"Triviality","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C2776333733","wikidata":"https://www.wikidata.org/wiki/Q3045336","display_name":"Fredholm determinant","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.22717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22717","pdf_url":"https://arxiv.org/pdf/2609.22717","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.2609.22717","doi":"https://doi.org/10.48550/arxiv.2609.22717","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.22717","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:2609.22717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22717","pdf_url":"https://arxiv.org/pdf/2609.22717","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214018737.pdf","grobid_xml":"https://content.openalex.org/works/W7214018737.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1631345926","https://openalex.org/W1669071243","https://openalex.org/W1873984302","https://openalex.org/W1931441370","https://openalex.org/W1938380508","https://openalex.org/W2022215767","https://openalex.org/W2022385268","https://openalex.org/W2107702031","https://openalex.org/W2142583931","https://openalex.org/W2154851836","https://openalex.org/W2171842910","https://openalex.org/W2598139253","https://openalex.org/W2604003040","https://openalex.org/W2739598953","https://openalex.org/W2949807632","https://openalex.org/W3027265156","https://openalex.org/W3183110793","https://openalex.org/W4376891850","https://openalex.org/W4384155149","https://openalex.org/W4393027573","https://openalex.org/W4407861112","https://openalex.org/W4412923328","https://openalex.org/W4417455135"],"related_works":["https://openalex.org/W4376891850","https://openalex.org/W4392319112","https://openalex.org/W4225718795","https://openalex.org/W2577581204","https://openalex.org/W3183110793","https://openalex.org/W2077957495","https://openalex.org/W4412923328","https://openalex.org/W2136419735","https://openalex.org/W2071156680","https://openalex.org/W3103110983"],"abstract_inverted_index":{"We":[0,87],"develop":[1],"a":[2,28,79,97],"probabilistic":[3,81],"construction":[4],"of":[5,18,22,71,83,100],"Toda":[6,36,75,129,148,165],"field":[7],"theory":[8],"correlators":[9,76],"from":[10],"the":[11,35,47,54,61,74,84,92,101,115,122,146,153,163],"Coulomb":[12],"gas":[13],"representation.":[14],"Reinterpreting":[15],"$n$-point":[16],"functions":[17],"primaries":[19],"as":[20],"$w$-moments":[21],"random":[23,49,102],"variables":[24],"with":[25],"respect":[26],"to":[27,89,158],"Gaussian":[29],"measure,":[30],"we":[31,131],"derive":[32],"constraints":[33,52,66],"on":[34,53],"momenta":[37],"and":[38,42,56,77,161],"coupling":[39],"constant.":[40],"$L^2$":[41],"$L^p$":[43],"convergence":[44,72,106],"conditions":[45,59,136,156],"for":[46,60,73],"associated":[48],"variables,":[50],"triviality":[51],"correlators,":[55],"local":[57,105,110],"integrability":[58,111,155],"cross-moments":[62],"are":[63],"derived.":[64],"These":[65],"define":[67],"an":[68],"extended":[69],"region":[70],"provide":[78],"systematic,":[80],"interpretation":[82],"Seiberg":[85],"bounds.":[86],"proceed":[88],"analytically":[90],"continue":[91],"moment":[93],"indices":[94],"by":[95],"employing":[96],"Mellin-Barnes":[98],"representation":[99],"variables.":[103],"The":[104],"boundaries":[107],"become":[108],"meromorphic":[109],"divisors,":[112],"and,":[113],"in":[114,137],"semiclassical":[116,139],"$b\\to0$":[117],"limit,":[118],"these":[119,151],"divisors":[120,160],"reconstruct":[121],"Liouville":[123],"charge":[124,166],"pole":[125,167],"lattice.":[126],"For":[127],"$A_n$":[128],"theory,":[130],"show":[132],"that":[133],"natural":[134],"$W_n$-closure":[135],"this":[138],"limit":[140],"select":[141],"rank-one,":[142],"Virasoro-like":[143],"submodules":[144],"inside":[145],"full":[147],"theory.":[149],"On":[150],"slices,":[152],"scalar":[154],"reduce":[157],"Liouville-like":[159],"recover":[162],"corresponding":[164],"lattices.":[168]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}