The diffusion limit for reversible jump processes onZ d with ergodic random bond conductivities

Finite difference approximations for partial differential equations with rapidly oscillating coefficients

“…In the next section we introducé the abstract framework and summarize the relevant results from [6] that we need. In section 3.2 we review the fini te différence version of the results in [6], as carried out in detail in [18] and in [19]. Our main theorems are stated in section 3.3 along with their proof.…”

“…The interesting case to consider is when h = e, that is h = er with r = (r ls r 2 , ..., r d ) fixed and with positive components. Then we have the discrete homogenization problem studied by Kuhnemann [18] and in [19].…”

“…There may, of course, be other ways of doing the discretization and the sampling that do capture homogenization effectively. In section 3 we present our main results for the multidimensional problem after introducing the relevant ideas from [6] and their fînite différence version [18,19].…”

Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder

“…In the uniformly elliptic case we consider here the infinite volume annealed homogenization result is well known [14], [11], [10], [3], and the effective diffusion matrix D of X(t) = X(t, ξ) is defined by…”

Tail estimates for homogenization theorems in random media

“…Weaker versions of the invariance principle already appeared in [19][20][21]. Let D 0 be the diffusion matrix of the limiting Brownian motion.…”