{"id":"https://openalex.org/W7225567929","doi":"https://doi.org/10.5281/zenodo.24063847","title":"Positive drift for a bi-invariant metric on a free group","display_name":"Positive drift for a bi-invariant metric on a free group","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225567929","doi":"https://doi.org/10.5281/zenodo.24063847"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24063847","doi":"https://doi.org/10.5281/zenodo.24063847","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24063847","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24063847","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041315596","display_name":"Yitzchak Shmalo","orcid":"https://orcid.org/0000-0002-2886-3049","observed_orcids":["https://orcid.org/0000-0002-2886-3049"]},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Shmalo, Yitzchak","raw_affiliation_strings":["Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041315596"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.7060999870300293,"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":0.7060999870300293,"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":0.13040000200271606,"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":0.08789999783039093,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/positive-drift","display_name":"positive drift","score":0.8080000281333923},{"id":"https://openalex.org/keywords/symmetric-random-walk","display_name":"symmetric random walk","score":0.7639999985694885},{"id":"https://openalex.org/keywords/free-groups","display_name":"free groups","score":0.699999988079071},{"id":"https://openalex.org/keywords/bi-invariant-metrics","display_name":"bi-invariant metrics","score":0.9890000224113464},{"id":"https://openalex.org/keywords/entropy-equation","display_name":"entropy equation","score":0.6779999732971191},{"id":"https://openalex.org/keywords/countable-groups","display_name":"countable groups","score":0.6330000162124634}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8632000088691711},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6955000162124634},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6610000133514404},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5526999831199646},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.49869999289512634},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48510000109672546},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4787999987602234},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.46149998903274536},{"id":"https://openalex.org/C77021192","wikidata":"https://www.wikidata.org/wiki/Q431078","display_name":"Free group","level":3,"score":0.45100000500679016},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.41850000619888306},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4050999879837036},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3443000018596649},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C559843788","wikidata":"https://www.wikidata.org/wiki/Q374268","display_name":"Infinite group","level":3,"score":0.273499995470047},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24063847","doi":"https://doi.org/10.5281/zenodo.24063847","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24063847","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24063848","doi":"https://doi.org/10.5281/zenodo.24063848","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24063848","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24063847","doi":"https://doi.org/10.5281/zenodo.24063847","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24063847","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1977994726","https://openalex.org/W2121179660","https://openalex.org/W1639352579","https://openalex.org/W2037832421","https://openalex.org/W2019970450","https://openalex.org/W2963826360","https://openalex.org/W98619662","https://openalex.org/W1615934027","https://openalex.org/W2515077078","https://openalex.org/W1562326240"],"abstract_inverted_index":{"Bj\u00f6rklund":[0],"asked":[1],"whether":[2],"the":[3,30,39,43,53,69,73,87,90,103],"drift":[4,88],"of":[5,56,89,105],"a":[6,11,63,78,116],"symmetric":[7],"random":[8],"walk":[9],"on":[10,42],"countable":[12],"group":[13,32],"vanishes":[14],"for":[15,110],"every":[16,81],"bi-invariant":[17,79],"metric":[18],"with":[19,34,92],"finite":[20],"first":[21,117],"moment.":[22],"We":[23],"show":[24],"that":[25,58,68],"it":[26],"does":[27],"not.":[28],"On":[29],"free":[31],"$\\mathbb{F}_r$":[33],"$r\\ge3$,":[35],"let":[36,50],"$\\mu$":[37],"be":[38,52,60],"uniform":[40],"measure":[41],"$2r$":[44],"generators":[45],"and":[46,49,86],"their":[47],"inverses,":[48],"$L(g)$":[51],"least":[54,98],"number":[55],"letters":[57],"must":[59],"deleted":[61],"from":[62],"word":[64,71],"representing":[65],"$g$":[66],"so":[67],"remaining":[70],"represents":[72],"identity.":[74],"Then":[75],"$d(g,h)=L(g^{-1}h)$":[76],"is":[77,96,102,115],"metric,":[80],"step":[82],"has":[83],"length":[84],"one,":[85],"$\\mu$-walk":[91],"respect":[93],"to":[94],"$d$":[95],"at":[97],"$c_r>0$,":[99],"where":[100],"$c_r$":[101],"root":[104],"an":[106],"explicit":[107],"entropy":[108],"equation;":[109],"instance":[111],"$c_{32}=1/2$.":[112],"The":[113],"proof":[114],"moment":[118],"bound":[119],"over":[120],"noncrossing":[121],"matchings.":[122]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}