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- W1534485097 abstract "We refer to [1] for notation. In [1], we proved that the first order correction for the hydrodynamic equation of symmetric simple exclusion processes with speed change in dimension d ≥ 3 is ∂ t ρ N =Δ u (ρ N (1+αρ N )) - ∂ uι 2(R ij (ρ N )∂ uj ρ N ), where R ij is a continuous function on (0, 1). We now prove that R = 0, which means that there is no correction of order N -1 to the hydrodynamic limit. Indeed, from Lemma 9.1 of [1], there exists a sequence of functions F i k that satisfies E vm [W 0,el τ x F i k ]=-R i,l (m)m(1 - m), where v m is the product Bernoulli measure of parameter m and W 0,el is the current between 0 and e l . Notice that v m is translation invariant. Therefore, since our process is gradient, we obtain E vm [W 0,el Σ τ x F i k ] = E vm [(Σ τ x W 0,el )F i k ] = 0, and thus R i,l (m) = 0. THEOREM 1. For symmetric simple exclusion processes with speed change, under diffusive rescaling, the density of particles q N (t, u) at time t around u ∈ R d satisfies N(q N (t, ) - m(t, )) → 0 for dimension d ≥ 3, where m(t, u) is the solution of the hydrodynamic limit ∂ ti m = Σ i ∂ 2 ui (m(1 + αm))." @default.
- W1534485097 created "2016-06-24" @default.
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- W1534485097 date "2002-04-01" @default.
- W1534485097 modified "2023-09-27" @default.
- W1534485097 title "Note about First order correction for the hydrodynamic limit of symmetric simple exclusion processes with speed change in dimension $d geq 3$" @default.
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- W1534485097 doi "https://doi.org/10.1214/aop/1023481015" @default.
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