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Hitting times and resistance distances in the hypercube.

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Title: Hitting times and resistance distances in the hypercube.
Authors: Sedlák, Jan1 (AUTHOR) deg.sedlak@gmail.com
Source: Journal of Physics A: Mathematical & Theoretical. 2026, Vol. 59 Issue 19, p1-13. 13p.
Subjects: Hypercubes, Electric resistance, Random walks, Combinatorics, Stochastic processes, Graph theory
Abstract: We study resistance distances (effective resistances) in the n -dimensional hypercube Qn. Closed forms are known for pairs of vertices at distance 1 (adjacent) and n (antipodal). We extend these results to all intermediate distances k, deriving identities that link hitting times and resistance distances across dimensions. In particular, we obtain a simple inter-dimensional recursion and an explicit representation of the resistance distance between vertices at distance k as a linear combination of resistance distances between adjacent vertices in hypercubes of lower dimension. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 193761359
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Hitting times and resistance distances in the hypercube.
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  Data: <searchLink fieldCode="AR" term="%22Sedlák%2C+Jan%22">Sedlák, Jan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> deg.sedlak@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+A%3A+Mathematical+%26+Theoretical%22">Journal of Physics A: Mathematical & Theoretical</searchLink>. 2026, Vol. 59 Issue 19, p1-13. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Hypercubes%22">Hypercubes</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+resistance%22">Electric resistance</searchLink><br /><searchLink fieldCode="DE" term="%22Random+walks%22">Random walks</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorics%22">Combinatorics</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We study resistance distances (effective resistances) in the n -dimensional hypercube Qn. Closed forms are known for pairs of vertices at distance 1 (adjacent) and n (antipodal). We extend these results to all intermediate distances k, deriving identities that link hitting times and resistance distances across dimensions. In particular, we obtain a simple inter-dimensional recursion and an explicit representation of the resistance distance between vertices at distance k as a linear combination of resistance distances between adjacent vertices in hypercubes of lower dimension. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Journal of Physics A: Mathematical & Theoretical is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1088/1751-8121/ae5859
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 13
        StartPage: 1
    Subjects:
      – SubjectFull: Hypercubes
        Type: general
      – SubjectFull: Electric resistance
        Type: general
      – SubjectFull: Random walks
        Type: general
      – SubjectFull: Combinatorics
        Type: general
      – SubjectFull: Stochastic processes
        Type: general
      – SubjectFull: Graph theory
        Type: general
    Titles:
      – TitleFull: Hitting times and resistance distances in the hypercube.
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            NameFull: Sedlák, Jan
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            – D: 15
              M: 05
              Text: 2026
              Type: published
              Y: 2026
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              Value: 59
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              Value: 19
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            – TitleFull: Journal of Physics A: Mathematical & Theoretical
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