Related papers: Record statistics for a discrete-time random walk …
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
In recent years, crowd analysis is important for applications such as smart cities, intelligent transportation system, customer behavior prediction, and visual surveillance. Understanding the characteristics of the individual motion in a…
The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the 1D lattice random walk in discrete time. We determine the survival probability of the random walker in…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…
A new class of one-dimensional, discrete time random walk model with memory, termed "Random walk with $n$ memory channels" (RW$n$MC) is proposed. In this model the information of $n$ ($n\in \mathbb{Z}$) previous steps from the walker's…
This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
The continuous time random walk model has been widely applied in various fields, including physics, biology, chemistry, finance, social phenomena, etc. In this work, we present an algorithm that utilizes a subordinate formula to generate…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
The strategic behaviour of pedestrians is largely determined by how they perceive and react to neighbouring people. This issue is addressed in this paper by a model which combines, in a time and space-dependent way, discrete and continuous…
In the context of countable groups of polynomial volume growth, we consider a large class of random walks that are allowed to take long jumps along multiple subgroups according to power law distributions. For such a random walk, we study…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
We study the record statistics of random walks after $n$ steps, $x_0, x_1,\ldots, x_n$, with arbitrary symmetric and continuous distribution $p(\eta)$ of the jumps $\eta_i = x_i - x_{i-1}$. We consider the age of the records, i.e. the time…
We calculate the explicit probability distribution function for the flux between sites in a simple discrete time diffusive system composed of independent random walkers. We highlight some of the features of the distribution and we discuss…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
We study the statistics of increments in record values in a time series $\{x_0=0,x_1, x_2, \ldots, x_n\}$ generated by the positions of a random walk (discrete time, continuous space) of duration $n$ steps. For arbitrary jump length…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…