Related papers: Random walk and Fibonacci matrices

We consider a symmetric random walk on the $\nu$-dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central limit theorem for this process. A short-range correction…

In this paper, we study a family of lattice walks which are related to the Hadamard conjecture. There is a bijection between paths of these walks which originate and terminate at the origin and equivalence classes of partial Hadamard…

Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in…

In this paper, we study properties of random walks on finite groups and later use them to obtain the limiting braid length expectation and component number of braid closure in a model of random braids, which is constructed by lifting…

Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…

We propose a family of lagged random walk sampling methods in simple undirected graphs, where transition to the next state (i.e. node) depends on both the current and previous states -- hence, lagged. The existing random walk sampling…

The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…

In this note, we design a discrete random walk on the real line which takes steps $0, \pm 1$ (and one with steps in $\{\pm 1, 2\}$) where at least $96\%$ of the signs are $\pm 1$ in expectation, and which has $\mathcal{N}(0,1)$ as a…

We consider a model for random walks on random environments (RWRE) with random subset of the d-dimensional Euclidean lattice as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the…

In one-dimensional random walks, the waiting time for each direction transitions is the same, even in the presence of bias, as a consequence of the microscopic-reversibility. We study the symmetry breaking of forward/ backward transition…

The set of visited sites and the number of visited sites are two basic properties of the random walk trajectory. We consider two independent random walks on a hyper-cubic lattice and study ordering probabilities associated with these…

Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…

We study three different random walk models on several two-dimensional lattices by Monte Carlo simulations. One is the usual nearest neighbor random walk. Another is the nearest neighbor random walk which is not allowed to backtrack. The…

We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…

The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…

Random walks are a series of up, down, and level steps that enumerate distinct paths from $(0,0)$ to $(2n,0)$, where $n$ is the semi-length of the path. We used these paths to analyze Catalan, Schr\"{o}der, and Motzkin number sequences…

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…

For a positive integer $n$, we study the number of steps to reach $n$ by a {\it Fibonacci walk} for some starting pair $a_1$ and $a_2$ satisfying the recurrence of $a_{k+2}=a_{k+1}+a_k$. The problem of slow Fibonacci walks, first suggested…

We study the expected distance of short uniform random walks in arbitrary dimensions with unit steps in random directions. It is known that for dimensions $d=2$ and $d=4$, all the moments of an $m$-step walk are integer. While for $d=2$,…

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…