Mixing Time of Random Walk on Poisson Geometry Small World
吳憲遠首都師範大學 下午 3:00–3:50 鴻經館 107 室Abstract
This talk focuses on the problem of modeling for small world effect on complex networks. We will consider the supercritical Poisson continuous percolation on d-dimensional torus T^d_n with volume n^d. By adding "long edges (short cuts)" randomly to the largest percolation cluster, we obtain a random graph G_n. Firstly, we show that the diameter of G_n grows at most polynomially fast in ln n and we call it the Poisson Geometry Small World. Secondly, we show that the random walk on G_n possesses the rapid mixing property, namely, the random walk mixes in time at most polynomially large in ln n.