We prove a local limit theorem for the probability of a site to be connected by disjoint paths to three points in subcritical Bernoulli percolation on Zd, d ≥ 2 in the limit where their distances tend to infinity.

We employ the Lévy sections theorem in the analysis of selected dollar exchange rate time series. The theorem is an extension of the classical central limit theorem and offers an alternative to the most usual analysis of the sum variable. We find that the presence of fat tails can be related to the local volatility pattern of the series.

We prove a local central limit theorem for “nonconventional” sums generated by some classes of sufficiently fast mixing sequences.

Cellular automata are a parallel and synchronous computing model, made of infinitely many finite automata updating according to the same local rule. Rice’s theorem states that any nontrivial property over computable functions is undecidable. It has been adapted by Kari to limit sets of cellular automata [Kar94], that is the set of configurations that can be reached arbitrarily late. This paper ...

To lower bound the effective dimension for local Hamiltonian models, we will use a theorem from [1, 2] as a stepping stone. This is a quantum version of the BerryEsseen theorem. The Berry-Esseen theorem is a more powerful statement than the central limit theorem, as it gives the rate of convergence of a distribution to a Gaussian. Let H = ∑ ν Eν |ν〉〈ν| be k-local, i.e., let H be of the form H =...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

Recently, Cartwright and Woess [5] provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type Ãn. Their results generalise results of Sawyer [18] where homogeneous trees are studied (these are Ã1 buildings), and Lindlbauer and Voit [9], where Ã2 buildings are studied. In this paper we apply techniques of spherical harmonic analysis to prove a local ...