The local time of simple random walks and Gaussian free fields in two dimensions

By using the method of probability analysis, we have researched the local time of a multidimensional-simple random walk. Note that the local time means the number of visits of a simple random walk to specific points in integer lattice. It is known that functionals of a local time and Gaussian free fields denote a variety of nonlinear and mathematical phenomena such as random media. Then, we are observing the relationship between two processes.
As a first step, we especially observe favorite points (the singular sites where the local time is large) et al. By A.Dembo, Y.Peres, O.Zeitouni, J.Rosen, who are leading experts in this field, the importance of this point has been recently shown.