Quenched scaling limits of trap models
نویسندگان
چکیده
Abstract. Fix a strictly positive measure W on the d-dimensional torus T. For an integer N ≥ 1, denote by W x , x = (x1, . . . , xd), 0 ≤ xi < N , the W measure of the cube [x/N, (x+1)/N), where 1 is the vector with all components equal to 1. In dimension 1, we prove that the hydrodynamic behavior of a superposition of independent random walks, in which a particle jumps from x/N to one of its neighbors at rate (NW x ) , is described in the diffusive scaling by the linear differential equation ∂tρ = (d/dW )(d/dx)ρ. In dimension d > 1, if W is a finite discrete measure, W = P
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