Parity properties and terminal points for lattice walks with steps of equal length

Visible Lattice Points in Random Walks

We consider the possible visits to visible points of a random walker moving up and right in the integer lattice (with probability α and 1 − α, respectively) and starting from the origin. We show that, almost surely, the asymptotic proportion of strings of k consecutive visible lattice points visited by such an α-random walk is a certain constant ck(α), which is actually an (explicitly calculabl...

Random Walks on Nite Convex Sets of Lattice Points

Random Walks with Decreasing Steps

We consider a one-dimensional random walk beginning at the origin and moving ± cn at time n. If ∑ cn < ∞ then with probability one the random walk has a final location. We describe the distribution of the final location and find the cumulants and the moments in terms of the power sums of the step sizes. Some interesting definite integrals involving infinite products of trigonometric functions c...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Branching annihilating random walks with parity conservation on a square lattice

Using Monte Carlo simulations we have studied the transition from an “active” steady state to an absorbing “inactive” state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the first model the randomly walking particles annihilate when they meet and the branching process creates two additional particles; in the second case we distingui...