Mixing of the symmetric beta-binomial splitting process on arbitrary graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916419409543168 |
|---|---|
| author | Pymar, Richard Rivera, Nicolás |
| author_facet | Pymar, Richard Rivera, Nicolás |
| contents | We study the mixing time of the symmetric beta-binomial splitting process on finite weighted connected graphs $G=(V,E,\{r_e\}_{e\in E})$ with vertex set $V$, edge set $E$ and positive edge-weights $r_e>0$ for $e\in E$. This is an interacting particle system with a fixed number of particles that updates through vertex-pairwise interactions which redistribute particles. We show that the mixing time of this process can be upper-bounded in terms of the maximal expected meeting time of two independent random walks on $G$. Our techniques involve using a process similar to the chameleon process invented by Morris (2006) to bound the mixing time of the exclusion process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02406 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mixing of the symmetric beta-binomial splitting process on arbitrary graphs Pymar, Richard Rivera, Nicolás Probability 60J27, 60K35, 82C22, 37A25 We study the mixing time of the symmetric beta-binomial splitting process on finite weighted connected graphs $G=(V,E,\{r_e\}_{e\in E})$ with vertex set $V$, edge set $E$ and positive edge-weights $r_e>0$ for $e\in E$. This is an interacting particle system with a fixed number of particles that updates through vertex-pairwise interactions which redistribute particles. We show that the mixing time of this process can be upper-bounded in terms of the maximal expected meeting time of two independent random walks on $G$. Our techniques involve using a process similar to the chameleon process invented by Morris (2006) to bound the mixing time of the exclusion process. |
| title | Mixing of the symmetric beta-binomial splitting process on arbitrary graphs |
| topic | Probability 60J27, 60K35, 82C22, 37A25 |
| url | https://arxiv.org/abs/2307.02406 |