Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.13549 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929251643555840 |
|---|---|
| author | Roy, Rishideep Saha, Kumarjit |
| author_facet | Roy, Rishideep Saha, Kumarjit |
| contents | We study coexistence in discrete time multi-type frog models.
We first show that for two types of particles on $\mathbb{Z}^d$, for $d\geq2$, for any jumping parameters $p_1, p_2 \in (0,1)$, coexistence occurs with positive probability for sufficiently rich deterministic initial configuration. We extend this to the case of random distribution of initial particles. We study the question of coexistence for multiple types and show positive probability coexistence of $2^d$ types on $\mathbb{Z}^d$ for rich enough initial configuration. We also show an instance of infinite coexistence on $\mathbb{Z}^d$ for $d \geq 3$ provided we have sufficiently rich initial configuration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_13549 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Coexistence in discrete time Multi-type competing Frog Models Roy, Rishideep Saha, Kumarjit Probability 60K35(Primary), 82B43(Secondary) We study coexistence in discrete time multi-type frog models. We first show that for two types of particles on $\mathbb{Z}^d$, for $d\geq2$, for any jumping parameters $p_1, p_2 \in (0,1)$, coexistence occurs with positive probability for sufficiently rich deterministic initial configuration. We extend this to the case of random distribution of initial particles. We study the question of coexistence for multiple types and show positive probability coexistence of $2^d$ types on $\mathbb{Z}^d$ for rich enough initial configuration. We also show an instance of infinite coexistence on $\mathbb{Z}^d$ for $d \geq 3$ provided we have sufficiently rich initial configuration. |
| title | Coexistence in discrete time Multi-type competing Frog Models |
| topic | Probability 60K35(Primary), 82B43(Secondary) |
| url | https://arxiv.org/abs/2012.13549 |