Uniform Convergence Ofmartingales in Theone - Dimensional Branchingrandom Walk

Almost Sure Convergence Rates for the Estimation of a Covariance Operator for Negatively Associated Samples

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...

The Dynami s of Multi - Spike Solutions to theOne - Dimensional Gierer -

Statistical uniform convergence in $2$-normed spaces

 The concept of statistical convergence in $2$-normed spaces for double sequence was introduced in [S. Sarabadan and S. Talebi, {it Statistical convergence of double sequences  in $2$-normed spaces }, Int. J. Contemp. Math. Sci. 6 (2011) 373--380]. In the first, we introduce concept strongly statistical convergence in $2$-normed spaces and generalize some results. Moreover,  we define the conce...

Convergence of the Length of the Loop-erased Random Walk on Finite Graphs to the Rayleigh Process

Let (Gn) ∞ n=1 be a sequence of finite graphs, and let Yt be the length of a loop-erased random walk on Gn after t steps. We show that for a large family of sequences of finite graphs, which includes the case in which Gn is the d-dimensional torus of size-length n for d ≥ 4, the process (Yt) ∞ t=0, suitably normalized, converges to the Rayleigh process introduced by Evans, Pitman, and Winter. O...

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...