We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold. In the present paper we give a proof of the full scaling limit for the weak invariance principle, improving the result in an earlier paper where we obtained a subsequential limit.

The non-linear invariance principle of Mossel, O’Donnell and Oleszkiewicz establishes that if fpx1, . . . , xnq is a multilinear low-degree polynomial with low influences then the distribution of fpB1, . . . ,Bnq is close (in various senses) to the distribution of fpG1, . . . ,Gnq, where Bi PR t ́1, 1u are independent Bernoulli random variables and Gi „ Np0, 1q are independent standard Gaussians...

In the context of uniform random mappings of an n-element set to itself, Aldous and Pitman (1994) established a functional invariance principle, showing that many n ! 1 limit distributions can be described as distributions of suitable functions of re ecting Brownian bridge. To study non-uniform cases, in this paper we formulate a sampling invariance principle in terms of iterates of a xed numbe...

Abstract: In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the weak invariance principle for partial sums of linear processes with short memory. We prove that whenever the partial sums of innovations satisfy th...