Related papers: Record statistics for a discrete-time random walk …

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number…

We consider several variants of a class of random walks whose increment distributions depend on the average value of the process over its most recent $N$ steps. We investigate the speed of the process, and in particular, the limiting speed…

Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from…

Novel aspects of human dynamics and social interactions are investigated by means of mobile phone data. Using extensive phone records resolved in both time and space, we study the mean collective behavior at large scales and focus on the…

We view random walks as the paths of foraging animals, perhaps searching for food or avoiding predators while forming a mental map of their surroundings. The formation of such maps requires them to memorise the locations they have visited.…

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

We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…

In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and…

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…

We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk.…

Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised--reactions emerge through various…

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…

The entropy of the random walk on the discrete contable group could be used for comparison of the system of the generators. Fundamental inequality between growth, entropy and escape gives the possibility to define "the best" system of the…

The integer points (sites) of the real line are marked by the positions of a standard random walk. We say that the set of marked sites is weakly, moderately or strongly sparse depending on whether the jumps of the standard random walk are…

We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. This is in contrast to the usual dynamical simple symmetric random walk in…

The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to now. A great deal of such theory focused on \textit{iid} or…

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…

We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…