Continuous-time vertex reinforced jump processes on Galton-Watson trees
A random walk \(X(t)\) with continuous time \(t\) is defined on the vertices of an infinite supercritical Galton-Watson tree with mean offspring that is finite and larger than one. Conditional on \(X(s)\) for values of \(s\) up to \(t\) where \(X(t)=u\), the process jumps to a neighbor \(v\) of \(u\) with transition rate proportional to the current duration time at \(v\) plus a positive constant \(c\). The critical value of \(c\) for recurrence/transience is proved to be unique and is explicitly given. The phase transitions are specified and compared to those of a discrete-time random walk in a certain random environment.
scientific article; zbMATH DE number 6083950