How two elephants can learn from each other
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911139075457024 |
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| author | Aguech, Rafik Qin, Shuo |
| author_facet | Aguech, Rafik Qin, Shuo |
| contents | We consider a two-elephant walking model in which the elephants interact dynamically. At each time step, each elephant determines its next move randomly based on its partner's past movements. We show that the asymptotic behavior of the elephants mainly depends on the sign and the absolute value of the product of their reinforcement parameters. In various regimes, we establish the law of large numbers and the central limit theorem. Our proofs are based on a connection to the random recursive trees and employ stochastic approximation techniques and martingale methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04862 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How two elephants can learn from each other Aguech, Rafik Qin, Shuo Probability 60K35, 60G42, 60F05, 60F15 We consider a two-elephant walking model in which the elephants interact dynamically. At each time step, each elephant determines its next move randomly based on its partner's past movements. We show that the asymptotic behavior of the elephants mainly depends on the sign and the absolute value of the product of their reinforcement parameters. In various regimes, we establish the law of large numbers and the central limit theorem. Our proofs are based on a connection to the random recursive trees and employ stochastic approximation techniques and martingale methods. |
| title | How two elephants can learn from each other |
| topic | Probability 60K35, 60G42, 60F05, 60F15 |
| url | https://arxiv.org/abs/2509.04862 |