{"id":"https://openalex.org/W7214036222","doi":"https://doi.org/10.48550/arxiv.2609.22499","title":"Conditional Stable Laws and Rare-Event Limits for Absorbing Markov Chains","display_name":"Conditional Stable Laws and Rare-Event Limits for Absorbing Markov Chains","publication_year":2026,"publication_date":"2026-09-18","ids":{"openalex":"https://openalex.org/W7214036222","doi":"https://doi.org/10.48550/arxiv.2609.22499"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.22499","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22499","pdf_url":"https://arxiv.org/pdf/2609.22499","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/2609.22499","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091998605","display_name":"Bernat Bassols-Cornudella","orcid":"https://orcid.org/0000-0001-6620-6739","observed_orcids":["https://orcid.org/0000-0001-6620-6739"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cornudella, Bernat Bassols","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036606341","display_name":"Matheus M. Castro","orcid":"https://orcid.org/0000-0002-2513-2830","observed_orcids":["https://orcid.org/0000-0002-2513-2830"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Castro, Matheus M","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":1,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9291999936103821,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9291999936103821,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.04270000010728836,"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/T13500","display_name":"Probability and Statistical Research","score":0.017899999395012856,"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/absorbing-markov-chains","display_name":"absorbing Markov chains","score":0.9620000123977661},{"id":"https://openalex.org/keywords/conditional-limit-theorems","display_name":"conditional limit theorems","score":0.8980000019073486},{"id":"https://openalex.org/keywords/rare-events","display_name":"rare events","score":0.6729999780654907},{"id":"https://openalex.org/keywords/stable-laws","display_name":"stable laws","score":0.671999990940094},{"id":"https://openalex.org/keywords/poisson-random-measure","display_name":"Poisson random measure","score":0.8029999732971191},{"id":"https://openalex.org/keywords/point-processes","display_name":"point processes","score":0.7350000143051147},{"id":"https://openalex.org/keywords/conditional-central-limit-theorem","display_name":"conditional central limit theorem","score":0.7960000038146973},{"id":"https://openalex.org/keywords/shrinking-targets","display_name":"shrinking targets","score":0.9229999780654907},{"id":"https://openalex.org/keywords/lean-4-formalization","display_name":"Lean 4 formalization","score":0.6200000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8233000040054321},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6409000158309937},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6148999929428101},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5860000252723694},{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.5449000000953674},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5424000024795532},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.45239999890327454},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.43529999256134033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43299999833106995},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4250999987125397},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.41769999265670776},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.3619999885559082},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C21430997","wikidata":"https://www.wikidata.org/wiki/Q5159279","display_name":"Conditional variance","level":4,"score":0.3427000045776367},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33640000224113464},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3140999972820282},{"id":"https://openalex.org/C103982235","wikidata":"https://www.wikidata.org/wiki/Q7309594","display_name":"Regular conditional probability","level":4,"score":0.3125999867916107},{"id":"https://openalex.org/C44492722","wikidata":"https://www.wikidata.org/wiki/Q327069","display_name":"Conditional probability","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29809999465942383},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2892000079154968},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.2720000147819519},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.259799987077713},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.25270000100135803},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.22499","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22499","pdf_url":"https://arxiv.org/pdf/2609.22499","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.2609.22499","doi":"https://doi.org/10.48550/arxiv.2609.22499","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.22499","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.22499","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22499","pdf_url":"https://arxiv.org/pdf/2609.22499","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/G2019088203","display_name":null,"funder_award_id":"2025/26997-9","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320283","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10"},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214036222.pdf","grobid_xml":"https://content.openalex.org/works/W7214036222.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W352919023","https://openalex.org/W1460189015","https://openalex.org/W1533415759","https://openalex.org/W1575147392","https://openalex.org/W1767588846","https://openalex.org/W1968548276","https://openalex.org/W1970320228","https://openalex.org/W1973454276","https://openalex.org/W1973485566","https://openalex.org/W1980019479","https://openalex.org/W1980620433","https://openalex.org/W1985371496","https://openalex.org/W2021506853","https://openalex.org/W2023753768","https://openalex.org/W2042801280","https://openalex.org/W2046646410","https://openalex.org/W2048212809","https://openalex.org/W2050579872","https://openalex.org/W2053366112","https://openalex.org/W2067601052","https://openalex.org/W2072442443","https://openalex.org/W2080562923","https://openalex.org/W2084247969","https://openalex.org/W2086061993","https://openalex.org/W2093175845","https://openalex.org/W2095912216","https://openalex.org/W2109246257","https://openalex.org/W2132403748","https://openalex.org/W2323545475","https://openalex.org/W2324802422","https://openalex.org/W2494822901","https://openalex.org/W2498839538","https://openalex.org/W2547199782","https://openalex.org/W2605906613","https://openalex.org/W2614665469","https://openalex.org/W2756143894","https://openalex.org/W2802739963","https://openalex.org/W2964211431","https://openalex.org/W2980199986","https://openalex.org/W3032832535","https://openalex.org/W3039641802","https://openalex.org/W3137342168","https://openalex.org/W4246042613","https://openalex.org/W4253840677","https://openalex.org/W4280501502","https://openalex.org/W4300920051","https://openalex.org/W4387016190","https://openalex.org/W4389615105","https://openalex.org/W4391463073","https://openalex.org/W4395084495","https://openalex.org/W4396645844","https://openalex.org/W4400105168","https://openalex.org/W4403747538","https://openalex.org/W4404750630","https://openalex.org/W4407425892","https://openalex.org/W4413297133","https://openalex.org/W4413880751","https://openalex.org/W4415334130","https://openalex.org/W7124166697","https://openalex.org/W7163016549"],"related_works":["https://openalex.org/W4280501502","https://openalex.org/W2323545475","https://openalex.org/W4226150061","https://openalex.org/W7099626584","https://openalex.org/W7096118562","https://openalex.org/W1995794737","https://openalex.org/W2072442443","https://openalex.org/W2140217508","https://openalex.org/W7052946460","https://openalex.org/W7096712834"],"abstract_inverted_index":{"We":[0,20,75],"establish":[1,77],"conditional":[2,79,94],"limit":[3,68,81],"theorems,":[4],"pointwise":[5],"in":[6,109],"the":[7,29,41,62,70],"initial":[8],"state,":[9],"for":[10,58,83,89,97],"absorbing":[11],"Markov":[12],"chains":[13],"on":[14],"a":[15,48,66,78,93],"compact":[16],"metric":[17],"space":[18],"$M$.":[19],"assume":[21],"$L^1(M,\u03c1)$-continuous":[22],"transition":[23],"densities,":[24],"irreducibility":[25],"and":[26,92,104],"aperiodicity.":[27],"For":[28],"observable":[30],"$f_\u03b2(x)=d_M(x,x_0)^{-\u03b2}$,":[31],"with":[32,69],"suitable":[33],"$x_0$":[34],"satisfying":[35],"$\u03c1(B_r(x_0))\\sim":[36],"C_d(x_0)r^d$,":[37],"we":[38],"prove":[39],"that":[40],"point-process":[42],"of":[43],"normalised":[44],"observations":[45],"converges":[46],"to":[47,99],"Poisson":[49,95],"random":[50],"measure.":[51],"This":[52],"yields":[53],"totally":[54],"right-skewed":[55],"$\u03b1$-stable":[56],"laws":[57],"$\u03b1=d/\u03b2\\in(0,2)$":[59],"and,":[60],"at":[61],"boundary":[63],"value":[64],"$\u03b1=2$,":[65],"Gaussian":[67],"non-standard":[71],"normalisation":[72],"$\\sqrt{n\\log":[73],"n}$.":[74],"also":[76],"central":[80],"theorem":[82],"$L^2$":[84],"observables,":[85],"exponential":[86],"deviation":[87],"bounds":[88],"bounded":[90],"observables":[91],"law":[96],"visits":[98],"shrinking":[100],"targets.":[101],"The":[102],"results":[103],"remarks":[105],"have":[106],"been":[107],"formalised":[108],"Lean~4.":[110]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-23T00:00:00"}