A kinetic model approximation of Walsh's spider process on the infinite star graph

We consider processes of deterministic motions on $ \mathit{k} $ copies of the star graph $ S_\mathit{k}: = K_{1, \mathit{k}} $ with $ \mathit{k} $ edges which are perturbed by two stochastic mechanisms: one caused by interfaces located at the graphs' centers, the other describing jumps between different copies of the same edge. We prove, extending the main result of [ 9 ], that diffusing scaling of these processes leads in the limit to the Walsh spider process on $ S_\mathit{k} $.