Bose Statistics of Random Walks on Graphs

Bose Statistics of Random Walks on Graphs | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Bose Statistics of Random Walks on Graphs Manfred Harringer This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5780223/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We build probabilistic process models of motions on a finite graph. For particle statistics, at first we select a particle. Then we build a path of the particle along consecutive edges. Particles are distinguished. Single particles perform Markov chains. For Bose statistics, at first we select an edge as request for a path of a particle along the edge. Particles are not distinguished. The edges are randomly selected by probability weights, or they are triggered by circuits of courses in small steps on circles. We present examples for these process models. We obtain some results, which follow from the balance equation, a refinement of the corresponding balance equation for Markov chains. Quantum mechanics inhibits these process models, because there the annihilation of the zero state is zero. Random walk Bose statistics Fock states Markov chains balance equation harmonic oscillator Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5780223","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":399262578,"identity":"a40ebd7b-edba-4333-b873-843f1482cbde","order_by":0,"name":"Manfred Harringer","email":"data:image/png;base64,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","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"Manfred","middleName":"","lastName":"Harringer","suffix":""}],"badges":[],"createdAt":"2025-01-07 10:08:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5780223/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5780223/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73689237,"identity":"4a50c154-747f-4d82-8238-14cc23e5ed05","added_by":"auto","created_at":"2025-01-13 15:09:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":417738,"visible":true,"origin":"","legend":"","description":"","filename":"BoseStatisticsofRandomWalksonGraphs.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5780223/v1_covered_8fb95483-3975-4195-b0a5-cc6d7fcf701a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bose Statistics of Random Walks on Graphs","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Random walk, Bose statistics, Fock states, Markov chains, balance equation, harmonic oscillator","lastPublishedDoi":"10.21203/rs.3.rs-5780223/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5780223/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe build probabilistic process models of motions on a finite graph. 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