Consider the long-range percolation model on integer lattice Zd in which all nearest-neighbour edges are present and otherwise x y connected with probability qx,y:=1−exp(−|x−y|−s), independently of state other edges. Throughout regime where yields a locally-finite graph, (i.e. for s>d,) we determine spectral dimension associated simple random walk, apart from at exceptional value d=1, s=2, is d...
