For a random walk in uniformly elliptic and i.i.d. environment on Zd with d?4, we show that the quenched annealed large deviation rate functions agree any compact set contained boundary ?D?{x?Rd:|x|1=1} of their domain which does not intersect (d?2)-dimensional facets ?D, provided disorder is low enough (depending set). As consequence, obtain simple explicit formula for both such ?D at disorder...

A fixed point of a map is a point in its domain which satisfies the equation F (x) = x. It is clear that, for such a point to exist, the domain and range must have common points. We point out two things, first, that the problem of existence of fixed points is equivalent to the problem of the solution of equations of the form f(x) = 0. Indeed, given such an equation, we can add the variable x to...

domain completeness Let < A, α, γ, C > a Galois insertion. [Cousot & Cousot ’77,’79] f : C −→ C, f = α ◦ f ◦ γ : A −→ A (b.c.a. of f) and ρ=γ ◦ α α(x) x f αf(x) =fα(x) ⊥ ⊥ a > > a ρ correct for f f α f(x) αf(x) Adjoining Declassification and Attack Models by Abstract Interpretation – p.5/19 Abstract domain completeness Let < A, α, γ, C > a Galois insertion. [Cousot & Cousot ’77,’79] f : C −→ C,...