标题： 一种具有递增突变率的空间突变模型 显示英文标题

标题： A Spatial Mutation Model with Increasing Mutation Rates

摘要： 我们考虑一个癌症的空间模型，其中细胞是$d$维环面$\mathcal{T}=[0,L]^d$上的点，每个具有$k-1$次突变的细胞以速率$\mu_k$获得第$k$次突变。 我们将假设突变率$\mu_k$是递增的，并且当环面体积趋于无穷大时，我们找到第一个细胞获得$k$次突变的渐近等待时间。 本文推广了Foo、Leder和Schweinsberg关于等待$k\geq 3$次突变的结果，他们考虑了所有突变率$\mu_k$相同的情况。 此外，我们找到了某些突变率值下突变之间的空间距离的极限分布。 显示英文摘要

摘要： We consider a spatial model of cancer in which cells are points on the $d$-dimensional torus $\mathcal{T}=[0,L]^d$, and each cell with $k-1$ mutations acquires a $k$th mutation at rate $\mu_k$. We will assume that the mutation rates $\mu_k$ are increasing, and we find the asymptotic waiting time for the first cell to acquire $k$ mutations as the torus volume tends to infinity. This paper generalizes results on waiting for $k\geq 3$ mutations by Foo, Leder, and Schweinsberg, who considered the case in which all of the mutation rates $\mu_k$ were the same. In addition, we find the limiting distribution of the spatial distances between mutations for certain values of the mutation rates.