Characterization of flip process rules with the same trajectories
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915607526506496 |
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| author | Hng, Eng Keat |
| author_facet | Hng, Eng Keat |
| contents | Garbe, Hladký, Šileikis and Skerman [Ann. Inst. Henri Poincaré Probab. Stat., 60 (2024), pp. 2878-2922] recently introduced a general class of random graph processes called flip processes and proved that the typical evolution of these discrete-time random graph processes corresponds to certain continuous-time deterministic graphon trajectories. We obtain a complete characterization of the equivalence classes of flip process rules with the same graphon trajectories. As an application, we characterize the flip process rules which are unique in their equivalence classes. These include several natural families of rules such as the complementing rules, the component completion rules, the extremist rules, and the clique removal rules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19925 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterization of flip process rules with the same trajectories Hng, Eng Keat Combinatorics Probability 05C80 Garbe, Hladký, Šileikis and Skerman [Ann. Inst. Henri Poincaré Probab. Stat., 60 (2024), pp. 2878-2922] recently introduced a general class of random graph processes called flip processes and proved that the typical evolution of these discrete-time random graph processes corresponds to certain continuous-time deterministic graphon trajectories. We obtain a complete characterization of the equivalence classes of flip process rules with the same graphon trajectories. As an application, we characterize the flip process rules which are unique in their equivalence classes. These include several natural families of rules such as the complementing rules, the component completion rules, the extremist rules, and the clique removal rules. |
| title | Characterization of flip process rules with the same trajectories |
| topic | Combinatorics Probability 05C80 |
| url | https://arxiv.org/abs/2305.19925 |