Abstract We establish a quenched local central limit theorem for the dynamic random conductance model on $${\mathbb {Z}}^d$$ Z d only assuming ergodicity with respect to space-time shifts and moment condition. As key analytic ingredient we show Hö...

We study the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space. Since ultra-discrete limit can be regarded as a classical limit of a quantum object, it implies that a correspondence between classical and qua...

ELEMENTARY CLASSES RAMI GROSSBERG AND SEBASTIEN VASEY Abstract. In the context of abstract elementary classes (AECs) with a monster model, several possible definitions of superstability have appeared in the literature. Among them are no long splitting chains, uniqueness of limit models, and solvability. Under the assumption that the class is tame and stable, we show that (asymptotically) no lon...

We study perturbations of homogeneous linear difference systems over infinite fields with absolute values. The coefficient matrices the treated belong to commutative groups which do not need be bounded. present a general limit periodic transformation an arbitrarily given system such that obtained has non-almost solutions. also formulate corollaries show how presented construction perturbed impr...

We provide a variational derivation of the limit shape of minimal difference partitions and discuss the link with exclusion statistics. This paper is dedicated to Professor Leonid Pastur for his 70th anniversary. A partition of a natural integer E [1] is a decomposition of E as a sum of a nonincreasing sequence of positive integers {hj}, i.e., E = ∑ j hj such that hj ≥ hj+1, for j = 1, 2 . . .....