Return Probability of Random Walks on the T-fractal

Return probability of random walks provides useful information on forecasting the recurrence of extr-eme events. Fractal network is a good approximation of the real network system. In this paper, unbiased discrete random walk on the infinite T-fractal was studied and the focus is return probability. The generating functions of first-return probability for node with degree 1 and 3 were constructed respectively based on the adjacency informa-tion for nodes of T-fractal. Using generating function as a tool, explicit expressions for return probability in finite steps and the global mean first-return time were derived. Results show that return probability is less than 1 and the global mean first-return time is 47/6.