Let p(x, y) be the transition probability of an isotropic random walk on a tree, where each site has d [greater-or-equal, slanted]3 neighbors. We define a branching random walk by letting a particle at site x give birth to a new particle at site y at rate [lambda]dp(x, y), jump to y at rate...

The noisy voter model is a spin system on a graph which may be obtained from the basic voter model by adding spontaneous flipping from 0 to 1 and from 1 to 0 at each site. Using duality, we obtain exact formulas for some important time-dependent and equilibrium functionals of this process. By...