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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.05220 |
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| _version_ | 1866910637821526016 |
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| author | Rameh, Ons |
| author_facet | Rameh, Ons |
| contents | We investigate the mixing time of the asymmetric Zero Range process on the segment with a non-decreasing rate. We show that the cutoff holds in the totally asymmetric case with a convex flux, and also with a concave flux if the asymmetry is strong enough. We show that the mixing occurs when the macroscopic system reaches equilibrium. A key ingredient of the proof, of independent interest, is the hydrodynamic limit for irregular initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cutoff phenomenon for asymmetric zero range process with monotone rates Rameh, Ons Probability We investigate the mixing time of the asymmetric Zero Range process on the segment with a non-decreasing rate. We show that the cutoff holds in the totally asymmetric case with a convex flux, and also with a concave flux if the asymmetry is strong enough. We show that the mixing occurs when the macroscopic system reaches equilibrium. A key ingredient of the proof, of independent interest, is the hydrodynamic limit for irregular initial data. |
| title | Cutoff phenomenon for asymmetric zero range process with monotone rates |
| topic | Probability |
| url | https://arxiv.org/abs/2410.05220 |