{"id":"https://openalex.org/W7212832290","doi":"https://doi.org/10.48550/arxiv.2609.12820","title":"Moments Comparison Inequalities for Critical 2d Stochastic Heat Flow, Polymers and GMC","display_name":"Moments Comparison Inequalities for Critical 2d Stochastic Heat Flow, Polymers and GMC","publication_year":2026,"publication_date":"2026-09-11","ids":{"openalex":"https://openalex.org/W7212832290","doi":"https://doi.org/10.48550/arxiv.2609.12820"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.12820","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12820","pdf_url":"https://arxiv.org/pdf/2609.12820","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/2609.12820","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019159112","display_name":"Ziyang Liu","orcid":"https://orcid.org/0009-0000-4501-237X","observed_orcids":["https://orcid.org/0009-0000-4501-237X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ziyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5019424240","display_name":"Zuodi Xie","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Zuodi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.948199987411499,"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":0.948199987411499,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.017400000244379044,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.005799999926239252,"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/gaussian-multiplicative-chaos","display_name":"Gaussian multiplicative chaos","score":0.9509999752044678},{"id":"https://openalex.org/keywords/negative-moments","display_name":"negative moments","score":0.7319999933242798},{"id":"https://openalex.org/keywords/fractional-moments","display_name":"fractional moments","score":0.8930000066757202},{"id":"https://openalex.org/keywords/bootstrap-argument","display_name":"bootstrap argument","score":0.7689999938011169},{"id":"https://openalex.org/keywords/geometric-decomposition","display_name":"geometric decomposition","score":0.6880000233650208}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7998999953269958},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7972999811172485},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5896999835968018},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5756999850273132},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5275999903678894},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5171999931335449},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.5037000179290771},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.462799996137619},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46000000834465027},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.40529999136924744},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.39500001072883606},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3569999933242798},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.33379998803138733},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3156999945640564},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.12820","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12820","pdf_url":"https://arxiv.org/pdf/2609.12820","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.2609.12820","doi":"https://doi.org/10.48550/arxiv.2609.12820","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.12820","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:2609.12820","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.12820","pdf_url":"https://arxiv.org/pdf/2609.12820","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":[{"id":"https://openalex.org/F4320320279","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212832290.pdf","grobid_xml":"https://content.openalex.org/works/W7212832290.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4388617930","https://openalex.org/W6929543509","https://openalex.org/W4402954826","https://openalex.org/W4413182557","https://openalex.org/W7203465240","https://openalex.org/W7202356081","https://openalex.org/W4414385215","https://openalex.org/W4403996115","https://openalex.org/W3196501854","https://openalex.org/W4403996050"],"abstract_inverted_index":{"We":[0,77],"employ":[1],"a":[2,83,90],"Gaussian":[3,21,27],"convex":[4],"inequality":[5],"developed":[6],"in":[7,26,30,94,117],"[AC15],":[8],"[Che26],":[9],"[Gue22],":[10],"and":[11,89],"[FUMPC26]":[12],"to":[13,72,113],"establish":[14,78],"(one":[15],"sided)":[16],"moment":[17,110],"comparison":[18],"inequalities":[19],"for":[20,51,100,104],"multiplicative":[22,73,114],"chaos,":[23],"directed":[24],"polymers":[25],"environment":[28],"and,":[29],"particular,":[31],"the":[32,58,69,79,108,121],"Critical":[33,59],"2d":[34,60],"Stochastic":[35],"Heat":[36],"Flow":[37],"(SHF),":[38],"including":[39],"upper":[40],"bounds":[41,50,81],"on":[42],"negative":[43],"moments,":[44],"as":[45,47],"well":[46],"similar":[48],"lower":[49],"$p$-th":[52,109],"moments":[53],"with":[54],"$p\\in":[55],"(0,1)$.":[56],"For":[57],"SHF,":[61,103],"averaged":[62,102],"over":[63],"small":[64],"balls,":[65],"we":[66,97],"also":[67],"obtain":[68],"matching":[70],"(up":[71],"constants)":[74],"complementary":[75,80],"bounds.":[76],"using":[82],"bootstrap":[84],"argument":[85],"inspired":[86],"by":[87,120],"[DS10]":[88],"geometric":[91],"decomposition":[92],"introduced":[93],"[GT26].":[95],"Specifically,":[96],"prove":[98],"that":[99],"locally":[101],"every":[105],"$p\\in\\mathbb":[106],"R$,":[107],"is,":[111],"up":[112],"constants,":[115],"bounded":[116],"both":[118],"sides":[119],"$\\frac{p(p-1)}{2}$-th":[122],"power":[123],"of":[124],"its":[125],"second":[126],"moment.":[127]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-15T00:00:00"}
