论文标题
在离散时间多类型青蛙模型中共存
Coexistence in discrete time Multi-type competing Frog Models
论文作者
论文摘要
我们研究离散时间多类青蛙模型中的共存。 我们首先表明，对于$ \ mathbb {z}^d $上的两种类型的粒子，对于$ d \ geq2 $，对于任何跳跃参数$ p_1，p_2 \ in（0,1）$，共存具有积极的概率，以实现足够丰富的富富含确定性的初始配置。我们将其扩展到初始颗粒随机分布的情况下。我们研究多种类型的共存问题，并在$ \ mathbb {z}^d $上显示$ 2^d $类型的正概率共存，以提供足够的初始配置。我们还显示了$ \ mathbb {z}^d $ for $ d \ geq 3 $的无限共存实例，提供了我们足够丰富的初始配置。
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.
