Simultaneous Cutoff on the Multitype Configuration Model
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929281094909952 |
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| author | Fernley, John Gerencsér, Balázs |
| author_facet | Fernley, John Gerencsér, Balázs |
| contents | We find Gaussian cutoff profiles for the total variation distance to stationarity of a random walk on a multiplex network: a finite number of directed configuration models sharing a vertex set, each with its own bounded degree distribution and edge probability. Further we consider the minimal total variation distance over this space of possible doubly stochastic edge probabilities at each point in time. Looking at all possible dynamics simultaneously on one realisation of the random graph, we find that this sequence of minimal distances converges in probability to the same cutoff profile as the chain with entropy maximising transition probabilities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11213 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simultaneous Cutoff on the Multitype Configuration Model Fernley, John Gerencsér, Balázs Probability Primary 05C81, Secondary 05C80, 60J10 We find Gaussian cutoff profiles for the total variation distance to stationarity of a random walk on a multiplex network: a finite number of directed configuration models sharing a vertex set, each with its own bounded degree distribution and edge probability. Further we consider the minimal total variation distance over this space of possible doubly stochastic edge probabilities at each point in time. Looking at all possible dynamics simultaneously on one realisation of the random graph, we find that this sequence of minimal distances converges in probability to the same cutoff profile as the chain with entropy maximising transition probabilities. |
| title | Simultaneous Cutoff on the Multitype Configuration Model |
| topic | Probability Primary 05C81, Secondary 05C80, 60J10 |
| url | https://arxiv.org/abs/2403.11213 |