Diffusion-limited annihilating-coalescing systems
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918180693213184 |
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| author | Ahn, Sungwon Junge, Matthew Lyu, Hanbaek Reeves, Lily Richey, Jacob Sivakoff, David |
| author_facet | Ahn, Sungwon Junge, Matthew Lyu, Hanbaek Reeves, Lily Richey, Jacob Sivakoff, David |
| contents | We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly different jump rates. Upon colliding, like particles coalesce up to some cap and unlike particles annihilate. We describe a phase transition as the initial particle density is varied and provide estimates for the expected occupation time of the root. For the symmetric setting with no cap on coalescence, we prove that the limiting occupation probability of the root is asymptotic to 2/3 the occupation probability for classical coalescing random walk. This addresses an open problem from Stephenson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19333 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diffusion-limited annihilating-coalescing systems Ahn, Sungwon Junge, Matthew Lyu, Hanbaek Reeves, Lily Richey, Jacob Sivakoff, David Probability 60K35 We study a family of interacting particle systems with annihilating and coalescing reactions. Two types of particles are interspersed throughout a transitive unimodular graph. Both types diffuse as simple random walks with possibly different jump rates. Upon colliding, like particles coalesce up to some cap and unlike particles annihilate. We describe a phase transition as the initial particle density is varied and provide estimates for the expected occupation time of the root. For the symmetric setting with no cap on coalescence, we prove that the limiting occupation probability of the root is asymptotic to 2/3 the occupation probability for classical coalescing random walk. This addresses an open problem from Stephenson. |
| title | Diffusion-limited annihilating-coalescing systems |
| topic | Probability 60K35 |
| url | https://arxiv.org/abs/2305.19333 |