Limiting distributions of triangle counts in linear preferential attachment models
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913168469524480 |
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| author | Dey, Partha S. Terlov, Grigory |
| author_facet | Dey, Partha S. Terlov, Grigory |
| contents | We derive distributional approximations for the number of triangles in the linear preferential attachment model $\mathrm{PAM}(m,δ)$, where $m\ge 2$ and $δ>-m$, with explicit rates of convergence. The limiting distribution undergoes a phase transition from Gaussian to another nontrivial distribution, which we characterize explicitly. The asymptotic behavior is governed by the interplay between the hidden random environment and the mean-field interaction effect. In particular, our analysis also yields a continuous phase transition in the expected number of triangles as $δ$ varies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28776 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limiting distributions of triangle counts in linear preferential attachment models Dey, Partha S. Terlov, Grigory Probability Combinatorics We derive distributional approximations for the number of triangles in the linear preferential attachment model $\mathrm{PAM}(m,δ)$, where $m\ge 2$ and $δ>-m$, with explicit rates of convergence. The limiting distribution undergoes a phase transition from Gaussian to another nontrivial distribution, which we characterize explicitly. The asymptotic behavior is governed by the interplay between the hidden random environment and the mean-field interaction effect. In particular, our analysis also yields a continuous phase transition in the expected number of triangles as $δ$ varies. |
| title | Limiting distributions of triangle counts in linear preferential attachment models |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2605.28776 |