A directed graph G is nonderogatory if its adjacency matrix A is nonderogatory, i.e., the characteristic polynomial of A is equal to the minimal polynomial of A. We analyze the problem whether the coalescence of difans and diwheels is nonderogatory. Also, a formula for the characteristic polynomial of the coalescence of two directed graphs is presented. 2000 Mathematics Subject Classification: ...

We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since it is not known whether a strong solution to the Skorohod equation in Lipschitz domains exists. Then we prove that the distance between the two processes converges to zero w...

We are interested in stationary “fluid” random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exists a coalesc...