Related papers: Greedy walks on two lines
We consider the interlacement Poisson point process on the space of doubly-infinite Z^d-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least…
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…
We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random…
We consider a one dimensional random-walk-like process, whose steps are centered Gaussians with variances which are determined according to the sequence of arrivals of a Poisson process on the line. This process is decorated by independent…
We consider the random walk in an \emph{i.i.d.} random environment on the infinite $d$-regular tree for $d \geq 3$. We consider the tree as a Cayley graph of free product of finitely many copies of $\Zbold$ and $\Zbold_2$ and define the…
In this paper, we study the problem of finding the probability that the two-dimensional (biased) monotonic random walk crosses the line $y=\alpha x+d$, where $\alpha,d \geq 0$. A $\beta$-biased monotonic random walk moves from $(a,b)$ to…
Random search processes are instrumental in studying and understanding navigation properties of complex networks, food search strategies of animals, diffusion control of molecular processes in biological cells, and improving web search…
Deterministic walks over a random set of points in one and two dimensions (d=1,2) are considered. Points (``cities'') are randomly scattered in R^d following a uniform distribution. A walker (a ``tourist''), at each time step, goes to the…
Let G be a countable group which acts by isometries on a separable, but not necessarily proper, Gromov hyperbolic space X. We say the action of G is weakly hyperbolic if G contains two independent hyperbolic isometries. We show that a…
The concept of intransitiveness for games, which is the condition for which there is no first-player winning strategy can arise surprisingly, as happens in the Penney game, an extension of the heads or tails. Since a game can be converted…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
We consider a modified random walk which uses unvisited edges whenever possible, and makes a simple random walk otherwise. We call such a walk an edge-process. We assume there is a rule A, which tells the walk which unvisited edge to use…
We consider the Grover walk on a finite graph composed of two arbitrary simple graphs connected by one edge, referred to as a bridge. The parameter $\epsilon>0$ assigned at the bridge represents the strength of connectivity: if…
Given an initial point $x_0 \in \mathbb{R}^d$ and a sequence of vectors $v_1, v_2, \dots$ in $\mathbb{R}^d$, we define a greedy sequence by setting $x_{n} = x_{n-1} \pm v_n$ where the sign is chosen so as to minimize $\|x_n\|$. We prove…
Geographic routing is a routing paradigm, which uses geographic coordinates of network nodes to determine routes. Greedy routing, the simplest form of geographic routing forwards a packet to the closest neighbor towards the destination. A…
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is…
\begin{abstract} Greedy permutations, also known as Gonzalez Orderings or Farthest Point Traversals are a standard way to approximate $k$-center clustering and have many applications in sampling and approximating metric spaces. A greedy…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution…
Deterministic walk in an excited random environment is a non-Markov integer-valued process $(X_n)_{n=0}^{\infty}$, whose jump at time $n$ depends on the number of visits to the site $X_n$. The environment can be understood as stacks of…