Related papers: Prime numbers and random walks in a square grid

We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…

We analyze Jim Propp's P-machine, a simple deterministic process that simulates a random walk on $Z^d$ to within a constant. The proof of the error bound relies on several estimates in the theory of simple random walks and some careful…

The sequence of the primes $p$ for which a variety over $\mathbb{Q}$ has no $p$-adic point plays a fundamental role in arithmetic geometry. This sequence is deterministic, however, we prove that if we choose a typical variety from a family…

Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops…

We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As…

In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime…

Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in $\{0, \pm 1\}^2$: the generating function is D-finite if…

The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…

Random walks of n steps taken into independent uniformly random directions in a d-dimensional Euclidean space (d larger than 1), are named Dirichlet when their step lengths are distributed according to a Dirichlet law. The latter continuous…

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…

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 consider the problem of predicting an individual's identity from accelerometry data collected during walking. In a previous paper we introduced an approach that transforms the accelerometry time series into an image by constructing its…

Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…

We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…

We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is the trace of the (i - 1)-st walk. The sequence of bias vectors…

Random walks simulate the randomness of objects, and are key instruments in various fields such as computer science, biology and physics. The counter part of classical random walks in quantum mechanics are the quantum walks. Quantum walk…

A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen…

We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…

Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example…

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a…