论文标题
具有离散性引起过渡的系统的固定分布
Stationary distributions of systems with Discreteness Induced Transitions
论文作者
论文摘要
我们提供了一些自催化反应网络的理论分析，这些反应网络表现出离散诱导的转变现象（DITS）。我们讲话的网络家族包括著名的Togashi和Kaneko模型。我们证明了家庭中模型的积极复发，所有时刻的有限性和几何形状。对于某些参数值，我们找到了固定分布的分析表达式，并讨论体积缩放对链的固定行为的影响。我们发现DIT消失的体积的确切临界值。
We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discretely induced transitions (DITs). The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments, and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution, and discuss the effect of volume scaling on the stationary behavior of the chain. We find the exact critical value of the volume for which DITs disappear.
