The rapid mixing of random walks defined by an n-cube

AbstractInspired by the mutation operator in genetic algorithms, we construct a complete weighted graph G from the n-cube Qn. The eigenvalues and conductance of G are determined first, then we show the rapid mixing of the random walk on G

Group-walk random graphs

We introduce a construction that gives rise to a variety of ‘geometric’ finite random graphs, and describe connections to the Poisson boundary, Naim’s kernel, and Sznitman’s random interlacements

Convexity in random resistor networks

Journal ArticleThe bulk conductivity o*(p) of the bond lattice in Zd is considered, where the conductivity of the bonds is either 1 with probability p or e > 0 with probability 1 - p. Rigorous and non-rigorous results demonstrating convexity of o*(p) near the percolation threshold pc are presented