3 problems

Let $G=(V,E)$ be a graph, let $G^\times=G\mathbin{\square}\mathbbm{Z}$ be its Cartesian product with the one-dimensional lattice, and let $p\in(0,1)$. In Bernoulli percolation on…

Consider the stochastic discrete-time SIR model with population size $N$, reproductive number $R_0$, and infection growth rate … When $\alpha<1$ (equivalently, $R_0<1$), the mean t…

Let $\beta,\mu,\gamma$ be the SIS model parameters, let $N$ be the population size, and set … When $\alpha<1$, the quasi-stationary distribution describes the long-term transient b…