{"id":"https://openalex.org/W4417466896","doi":"https://doi.org/10.48550/arxiv.2512.14152","title":"Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers","display_name":"Persistence probabilities of MA(1) sequences with Laplace innovations and $q$-deformed zigzag numbers","publication_year":2025,"publication_date":"2025-12-16","ids":{"openalex":"https://openalex.org/W4417466896","doi":"https://doi.org/10.48550/arxiv.2512.14152"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2512.14152","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.14152","pdf_url":"https://arxiv.org/pdf/2512.14152","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/2512.14152","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032794732","display_name":"Frank Aurzada","orcid":"https://orcid.org/0000-0002-4465-0297","observed_orcids":["https://orcid.org/0000-0002-4465-0297"]},"institutions":[{"id":"https://openalex.org/I31512782","display_name":"Technische Universit\u00e4t Darmstadt","ror":"https://ror.org/05n911h24","country_code":"DE","type":"education","lineage":["https://openalex.org/I31512782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Aurzada, Frank","raw_affiliation_strings":["Technical University of Darmstadt , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technical University of Darmstadt , Germany","institution_ids":["https://openalex.org/I31512782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066885076","display_name":"Kilian Raschel","orcid":"https://orcid.org/0000-0002-9303-3121","observed_orcids":["https://orcid.org/0000-0002-9303-3121"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I49451733","display_name":"Universit\u00e9 d'Angers","ror":"https://ror.org/04yrqp957","country_code":"FR","type":"education","lineage":["https://openalex.org/I49451733"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Raschel, Kilian","raw_affiliation_strings":["CNRS , Universit\u00e9 d'Angers , France ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS , Universit\u00e9 d'Angers , France ,","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I49451733"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"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/T13500","display_name":"Probability and Statistical Research","score":0.9193999767303467,"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"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.9193999767303467,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.025200000032782555,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.009499999694526196,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/persistence-probability","display_name":"persistence probability","score":0.9789999723434448},{"id":"https://openalex.org/keywords/ma-1-process","display_name":"MA(1) process","score":0.8930000066757202},{"id":"https://openalex.org/keywords/moving-average-processes","display_name":"moving average processes","score":0.8539999723434448},{"id":"https://openalex.org/keywords/q-pochhammer-symbol","display_name":"q-Pochhammer symbol","score":0.8709999918937683},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.9769999980926514}],"concepts":[{"id":"https://openalex.org/C2781009140","wikidata":"https://www.wikidata.org/wiki/Q7170389","display_name":"Persistence (discontinuity)","level":2,"score":0.7829999923706055},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.7778000235557556},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.734000027179718},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.6987000107765198},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5627999901771545},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5564000010490417},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5353999733924866},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45899999141693115},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.42500001192092896},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.4036000072956085},{"id":"https://openalex.org/C22243797","wikidata":"https://www.wikidata.org/wiki/Q2058297","display_name":"Laplace's method","level":3,"score":0.3560999929904938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3181999921798706},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2799000144004822},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.263700008392334},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2512.14152","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.14152","pdf_url":"https://arxiv.org/pdf/2512.14152","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":"pmh:oai:HAL:hal-05844982v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05844982","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2512.14152","doi":"https://doi.org/10.48550/arxiv.2512.14152","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.14152","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:2512.14152","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.14152","pdf_url":"https://arxiv.org/pdf/2512.14152","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/G525087652","display_name":"Conditioning and limit theorems for random walks and branching processes","funder_award_id":"ANR-23-CE40-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4417466896.pdf","grobid_xml":"https://content.openalex.org/works/W4417466896.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4377111682","https://openalex.org/W4415313832"],"related_works":["https://openalex.org/W4415313832","https://openalex.org/W7212023145","https://openalex.org/W4400518976","https://openalex.org/W4225709183","https://openalex.org/W2599264124","https://openalex.org/W3171883780","https://openalex.org/W4366459374","https://openalex.org/W1994430878","https://openalex.org/W2896831533","https://openalex.org/W7100349050"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,47,51,62,66],"persistence":[3,21,52],"probabilities":[4,22,53],"of":[5,10,30,41,50,59,61],"a":[6,17],"moving":[7],"average":[8],"process":[9],"order":[11],"one":[12],"with":[13],"innovations":[14],"that":[15],"follow":[16],"Laplace":[18],"distribution.":[19],"The":[20],"can":[23,54],"be":[24,55],"computed":[25],"fully":[26],"explicitly":[27],"in":[28,57],"terms":[29,58],"classical":[31],"combinatorial":[32],"quantities":[33],"like":[34],"certain":[35],"$q$-Pochhammer":[36],"symbols":[37],"or":[38,65],"$q$-deformed":[39],"analogues":[40],"Euler's":[42],"zigzag":[43],"numbers,":[44],"respectively.":[45,69],"Similarly,":[46],"generating":[48],"functions":[49],"written":[56],"$q$-analogues":[60],"exponential":[63],"function":[64],"$q$-sine/$q$-cosine":[67],"functions,":[68]},"counts_by_year":[{"year":2026,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-12-18T00:00:00"}
