The averaging process on infinite graphs
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916355722182656 |
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| author | Gantert, Nina Vilkas, Timo |
| author_facet | Gantert, Nina Vilkas, Timo |
| contents | We consider the averaging process on an infinite connected graph with bounded degree and independent, identically distributed starting values or initial opinions. Assuming that the law of the initial opinion of a vertex has a finite second moment, we show that the opinions of all vertices converge in $L^2$ to the first moment of the law of the initial opinions. A key tool in the proof is the Sharing a drink procedure introduced by Olle Häggström. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The averaging process on infinite graphs Gantert, Nina Vilkas, Timo Probability 60F25, 60K35 We consider the averaging process on an infinite connected graph with bounded degree and independent, identically distributed starting values or initial opinions. Assuming that the law of the initial opinion of a vertex has a finite second moment, we show that the opinions of all vertices converge in $L^2$ to the first moment of the law of the initial opinions. A key tool in the proof is the Sharing a drink procedure introduced by Olle Häggström. |
| title | The averaging process on infinite graphs |
| topic | Probability 60F25, 60K35 |
| url | https://arxiv.org/abs/2408.06859 |