arXiv subjects
Publications and source records attributed to Moran Cohen.
We prove a Harnack inequality for the solutions of a difference equation with non-elliptic balanced i.i.d. coefficients. Along the way we prove a (weak) quantitative homogenisation result, which we believe is of some interest too.
In this work, we discuss certain ballistic random walks in random environments on $\mathbb{Z}^d$, and prove the equivalence between the static and dynamic points of view in dimension $d\geq4$. Using this equivalence, we also prove a version of a local limit theorem which relates the local behavior of the quenched and annealed measures of the random walk by a prefactor.
There is much more known about the family of superstable theories when compared to stable theories. This calls for a search of an analogous "super-dependent" characterization in the context of dependent theories. This problem has been treated in \cite{Sh:783,Sh:863}, where the candidates "Strongly dependent", "Strongly dependent^2" and others were considered. These families generated new families when we are considering intersections with the stable family. Here, continuing \cite[§2, §5E,F,G]{Sh:863}, we deal with several candidates, defined using dividing properties and related ranks of types. Those candidates are subfamilies of "Strongly dependent". Fulfilling some promises from \cite{Sh:863} in particular \cite[1.4(4)]{Sh:863}, we try to make this self contained within reason by repeating some things from there. More specifically we fulfil some promises from \cite{Sh:863} to to give more details, in particular: in \S4 for \cite[1.4(4)]{Sh:863}, in \S2 for \cite[5.47(2)=Ldw5.35(2)]{Sh:863} and in \S1 for \cite[5.49(2)]{Sh:863}
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of stable theories. Stronger results are given for omega-stable.