{"id":"https://openalex.org/W7214384274","doi":"https://doi.org/10.48550/arxiv.2609.30045","title":"Recurrence and range of the balanced excited random walk M(2,1,2)","display_name":"Recurrence and range of the balanced excited random walk M(2,1,2)","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214384274","doi":"https://doi.org/10.48550/arxiv.2609.30045"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30045","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30045","pdf_url":"https://arxiv.org/pdf/2609.30045","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/2609.30045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113053514","display_name":"Shuo Qin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qin, Shuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113053514"],"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":0.9951000213623047,"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":0.9951000213623047,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0017999999690800905,"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":0.00019999999494757503,"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/excited-random-walks","display_name":"excited random walks","score":0.8199999928474426},{"id":"https://openalex.org/keywords/recurrence","display_name":"recurrence","score":0.6579999923706055},{"id":"https://openalex.org/keywords/range-of-random-walk","display_name":"range of random walk","score":0.6510000228881836}],"concepts":[{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.8779000043869019},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7059000134468079},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6904000043869019},{"id":"https://openalex.org/C154072304","wikidata":"https://www.wikidata.org/wiki/Q5747218","display_name":"Heterogeneous random walk in one dimension","level":3,"score":0.6762999892234802},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6240000128746033},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.6148999929428101},{"id":"https://openalex.org/C37727645","wikidata":"https://www.wikidata.org/wiki/Q6675770","display_name":"Loop-erased random walk","level":4,"score":0.5468000173568726},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5464000105857849},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5288000106811523},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5163999795913696},{"id":"https://openalex.org/C181500209","wikidata":"https://www.wikidata.org/wiki/Q215328","display_name":"Excited state","level":2,"score":0.5001000165939331},{"id":"https://openalex.org/C155155215","wikidata":"https://www.wikidata.org/wiki/Q7448025","display_name":"Self-avoiding walk","level":3,"score":0.4876999855041504},{"id":"https://openalex.org/C20353970","wikidata":"https://www.wikidata.org/wiki/Q1056998","display_name":"Simple random sample","level":3,"score":0.4837999939918518},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.367900013923645},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3091999888420105},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2637999951839447}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30045","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30045","pdf_url":"https://arxiv.org/pdf/2609.30045","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.2609.30045","doi":"https://doi.org/10.48550/arxiv.2609.30045","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30045","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:2609.30045","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30045","pdf_url":"https://arxiv.org/pdf/2609.30045","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214384274.pdf","grobid_xml":"https://content.openalex.org/works/W7214384274.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7099626105","https://openalex.org/W2949766453","https://openalex.org/W2043959104","https://openalex.org/W3134844824","https://openalex.org/W7098281195","https://openalex.org/W787198937","https://openalex.org/W2141877640","https://openalex.org/W2525632058","https://openalex.org/W2912034194","https://openalex.org/W3006492990"],"abstract_inverted_index":{"We":[0],"prove":[1,77],"that":[2],"the":[3,40,64,69,90],"planar":[4,30,70],"balanced":[5,80],"excited":[6,81],"random":[7,18,32,72,82],"walk":[8,13,19,33],"$M(2,1,2)$":[9],"is":[10],"recurrent.":[11],"This":[12],"takes":[14],"a":[15,29],"horizontal":[16],"simple":[17,31,71],"step":[20,34],"on":[21,35],"its":[22],"first":[23],"departure":[24],"from":[25],"each":[26,98],"vertex":[27,99],"and":[28,58,93],"every":[36,60],"later":[37],"departure.":[38],"Moreover,":[39],"number":[41],"of":[42,79],"distinct":[43],"vertices":[44],"visited":[45],"before":[46],"time":[47],"$n$,":[48],"multiplied":[49],"by":[50,102],"$(\\log":[51],"n)/n$,":[52],"converges":[53],"to":[54],"$\u03c0$":[55],"almost":[56],"surely":[57],"in":[59,84],"$L^p$,":[61],"$1\\le":[62],"p<\\infty$,":[63],"same":[65],"limit":[66],"as":[67],"for":[68],"walk.":[73],"More":[74],"generally,":[75],"we":[76],"recurrence":[78],"walks":[83],"spatially":[85],"inhomogeneous":[86],"cookie":[87,95],"environments":[88],"whenever":[89],"total":[91],"positive":[92],"negative":[94],"strengths":[96],"at":[97],"are":[100],"bounded":[101],"constants":[103],"$A,":[104],"B$":[105],"with":[106],"$A+B<1+1/(2\u03c0+1)$.":[107]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-26T00:00:00"}
