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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.04671 |
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| _version_ | 1866915835561377792 |
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| author | Braunsteins, Peter Mandjes, Michel Montalescot, Florian |
| author_facet | Braunsteins, Peter Mandjes, Michel Montalescot, Florian |
| contents | In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erdős--Rényi graph that is resampled every time unit, independently of the previous ones, with `edge existence probability' $p$. The population process consists of $M$ individuals which reside at the vertices of the dynamic graph. At each point in time any of the $M$ individuals, supposing it resides at a vertex with $k$ neighbors, jumps to an adjacent vertex with probability $k/(k+1)$ (where this adjacent vertex is picked uniformly at random), and with probability $1/(k+1)$ it stays where it is. We suppose we observe the numbers of individuals at each of the vertices, but not the evolving random graph itself. We propose two estimators for $p$, and establish their consistency and asymptotic normality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04671 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Estimating Graph Dynamics from Population Observations Braunsteins, Peter Mandjes, Michel Montalescot, Florian Probability Statistics Theory In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erdős--Rényi graph that is resampled every time unit, independently of the previous ones, with `edge existence probability' $p$. The population process consists of $M$ individuals which reside at the vertices of the dynamic graph. At each point in time any of the $M$ individuals, supposing it resides at a vertex with $k$ neighbors, jumps to an adjacent vertex with probability $k/(k+1)$ (where this adjacent vertex is picked uniformly at random), and with probability $1/(k+1)$ it stays where it is. We suppose we observe the numbers of individuals at each of the vertices, but not the evolving random graph itself. We propose two estimators for $p$, and establish their consistency and asymptotic normality. |
| title | Estimating Graph Dynamics from Population Observations |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2603.04671 |