Dissipative particle systems on expanders
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913835654316032 |
|---|---|
| author | Haslegrave, John Keevash, Peter |
| author_facet | Haslegrave, John Keevash, Peter |
| contents | We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet. We study the equilibrium time of the process, by which we mean the number of steps taken until no further interactions can occur. Under a rather general framework, we obtain high probability upper and lower bounds on the equilibrium time that match up to a constant factor and are of order $n\log n$ if there are order $n$ vertices and particles. We also obtain similar results for the balanced two-type annihilation model of chemical reactions; here, the balanced case (equal density of types) does not fit into our general framework and makes the analysis considerably more difficult. Our models do not admit any exact solution as for integrable systems or the duality approach available for some other particle systems, so we develop a variety of combinatorial tools for comparing processes in the absence of monotonicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dissipative particle systems on expanders Haslegrave, John Keevash, Peter Probability Mathematical Physics Combinatorics 05C81, 82C22, 60K35 We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet. We study the equilibrium time of the process, by which we mean the number of steps taken until no further interactions can occur. Under a rather general framework, we obtain high probability upper and lower bounds on the equilibrium time that match up to a constant factor and are of order $n\log n$ if there are order $n$ vertices and particles. We also obtain similar results for the balanced two-type annihilation model of chemical reactions; here, the balanced case (equal density of types) does not fit into our general framework and makes the analysis considerably more difficult. Our models do not admit any exact solution as for integrable systems or the duality approach available for some other particle systems, so we develop a variety of combinatorial tools for comparing processes in the absence of monotonicity. |
| title | Dissipative particle systems on expanders |
| topic | Probability Mathematical Physics Combinatorics 05C81, 82C22, 60K35 |
| url | https://arxiv.org/abs/2404.04149 |