Loewner’s Differential Equation and Spidernets

We regard Loewner’s differential equation with non-negative continuous driving functions (and more generally driving measures with non-negative support) from a quantum probability point of view and approximate the underlying quantum process by the adjacency matrices of growing graphs which arise from the comb product of certain spidernets. In the general case of an arbitrary continuous driving function we find a weaker approximation by comb products of graphs with weighted loops.