On the spectral dimension of random trees
We determine the spectral dimensions of a variety of ensembles of infinite trees. Common to the ensembles considered is that sample trees have a distinguished infinite spine at whose vertices branches can be attached according to some probability distribution. In particular, we consider a family of...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2006-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3507/pdf |
| _version_ | 1797270395586347008 |
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| author | Bergfinnur Durhuus Thordur Jonsson John Wheater |
| author_facet | Bergfinnur Durhuus Thordur Jonsson John Wheater |
| author_sort | Bergfinnur Durhuus |
| collection | DOAJ |
| description | We determine the spectral dimensions of a variety of ensembles of infinite trees. Common to the ensembles considered is that sample trees have a distinguished infinite spine at whose vertices branches can be attached according to some probability distribution. In particular, we consider a family of ensembles of $\textit{combs}$, whose branches are linear chains, with spectral dimensions varying continuously between $1$ and $3/2$. We also introduce a class of ensembles of infinite trees, called $\textit{generic random trees}$, which are obtained as limits of ensembles of finite trees conditioned to have fixed size $N$, as $N \to \infty$. Among these ensembles is the so-called uniform random tree. We show that generic random trees have spectral dimension $d_s=4/3$. |
| first_indexed | 2024-04-25T02:03:35Z |
| format | Article |
| id | doaj.art-0d933286ee184fcf90b5f358d63bd82b |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:03:35Z |
| publishDate | 2006-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-0d933286ee184fcf90b5f358d63bd82b2024-03-07T14:34:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502006-01-01DMTCS Proceedings vol. AG,...Proceedings10.46298/dmtcs.35073507On the spectral dimension of random treesBergfinnur Durhuus0Thordur Jonsson1John Wheater2Department of Mathematical Sciences [Copenhagen]Science InstituteRudolf Peierls Center for Theoretical PhysicsWe determine the spectral dimensions of a variety of ensembles of infinite trees. Common to the ensembles considered is that sample trees have a distinguished infinite spine at whose vertices branches can be attached according to some probability distribution. In particular, we consider a family of ensembles of $\textit{combs}$, whose branches are linear chains, with spectral dimensions varying continuously between $1$ and $3/2$. We also introduce a class of ensembles of infinite trees, called $\textit{generic random trees}$, which are obtained as limits of ensembles of finite trees conditioned to have fixed size $N$, as $N \to \infty$. Among these ensembles is the so-called uniform random tree. We show that generic random trees have spectral dimension $d_s=4/3$.https://dmtcs.episciences.org/3507/pdfspectral dimensionrandom combsrandom trees[info.info-ds] computer science [cs]/data structures and algorithms [cs.ds][info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Bergfinnur Durhuus Thordur Jonsson John Wheater On the spectral dimension of random trees Discrete Mathematics & Theoretical Computer Science spectral dimension random combs random trees [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | On the spectral dimension of random trees |
| title_full | On the spectral dimension of random trees |
| title_fullStr | On the spectral dimension of random trees |
| title_full_unstemmed | On the spectral dimension of random trees |
| title_short | On the spectral dimension of random trees |
| title_sort | on the spectral dimension of random trees |
| topic | spectral dimension random combs random trees [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/3507/pdf |
| work_keys_str_mv | AT bergfinnurdurhuus onthespectraldimensionofrandomtrees AT thordurjonsson onthespectraldimensionofrandomtrees AT johnwheater onthespectraldimensionofrandomtrees |