论文标题
可解决类别的更新过程
A solvable class of renewal processes
论文作者
论文摘要
当续签过程的到达时间的分布是几何定律的混合物时，我们证明该过程的更新功能是通过与混合分布明确相关的概率度量矩给出的。我们还在连续的情况下表现出类似的结果，即到达法则是指数定律的混合物。然后，我们观察到上述离散类别的更新过程提供了可解决的随机聚合物家族。也就是说，我们获得了固定在上述更新过程位置的聚合物的分配函数的确切表示。在混合度量是广义的弧形定律的特定情况下，可以明确处理计算。
When the distribution of the inter-arrival times of a renewal process is a mixture of geometric laws, we prove that the renewal function of the process is given by the moments of a probability measure which is explicitly related to the mixture distribution. We also present an analogous result in the continuous case when the inter-arrival law is a mixture of exponential laws. We then observe that the above discrete class of renewal processes provides a solvable family of random polymers. Namely, we obtain an exact representation of the partition function of polymers pinned at sites of the aforementioned renewal processes. In the particular case where the mixture measure is a generalized Arcsine law, the computations can be explicitly handled.
