The Uncover Process for Random Labeled Trees Article Swipe
Benjamin Hackl
,
Alois Panholzer
,
Stephan M. Wagner
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2301.00664
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2301.00664
We consider the process of uncovering the vertices of a random labeled tree according to their labels. First, a labeled tree with $n$ vertices is generated uniformly at random. Thereafter, the vertices are uncovered one by one, in order of their labels. With each new vertex, all edges to previously uncovered vertices are uncovered as well. In this way, one obtains a growing sequence of forests. Three particular aspects of this process are studied in this work: first the number of edges, which we prove to converge to a stochastic process akin to a Brownian bridge after appropriate rescaling. Second, the connected component of a fixed vertex, for which different phases are identified and limiting distributions determined in each phase. Lastly, the largest connected component, for which we also observe a phase transition.
Related Topics
Concepts
Vertex (graph theory)
Combinatorics
Random tree
Tree (set theory)
Mathematics
Limiting
Process (computing)
Sequence (biology)
Connected component
Stochastic process
Discrete mathematics
Computer science
Statistics
Graph
Engineering
Artificial intelligence
Chemistry
Mechanical engineering
Robot
Motion planning
Operating system
Biochemistry
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2301.00664
- https://arxiv.org/pdf/2301.00664
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4313484482
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4313484482Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2301.00664Digital Object Identifier
- Title
-
The Uncover Process for Random Labeled TreesWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-01-02Full publication date if available
- Authors
-
Benjamin Hackl, Alois Panholzer, Stephan M. WagnerList of authors in order
- Landing page
-
https://arxiv.org/abs/2301.00664Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2301.00664Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2301.00664Direct OA link when available
- Concepts
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Vertex (graph theory), Combinatorics, Random tree, Tree (set theory), Mathematics, Limiting, Process (computing), Sequence (biology), Connected component, Stochastic process, Discrete mathematics, Computer science, Statistics, Graph, Engineering, Artificial intelligence, Chemistry, Mechanical engineering, Robot, Motion planning, Operating system, BiochemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.vertices | 7, 23, 31, 51 |
| abstract_inverted_index.according | 13 |
| abstract_inverted_index.component | 102 |
| abstract_inverted_index.connected | 101, 123 |
| abstract_inverted_index.different | 109 |
| abstract_inverted_index.generated | 25 |
| abstract_inverted_index.uncovered | 33, 50, 53 |
| abstract_inverted_index.uniformly | 26 |
| abstract_inverted_index.component, | 124 |
| abstract_inverted_index.determined | 116 |
| abstract_inverted_index.identified | 112 |
| abstract_inverted_index.particular | 67 |
| abstract_inverted_index.previously | 49 |
| abstract_inverted_index.rescaling. | 98 |
| abstract_inverted_index.stochastic | 89 |
| abstract_inverted_index.uncovering | 5 |
| abstract_inverted_index.Thereafter, | 29 |
| abstract_inverted_index.appropriate | 97 |
| abstract_inverted_index.transition. | 132 |
| abstract_inverted_index.distributions | 115 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/15 |
| sustainable_development_goals[0].score | 0.75 |
| sustainable_development_goals[0].display_name | Life in Land |
| citation_normalized_percentile |