Related papers: Scaling Mobility Patterns and Collective Movements…
The distribution of the first positive position reached by a random walker starting at the origin is central to the analysis of extremes and records in one-dimensional random walks. In this work, we present a detailed and self-contained…
For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations.…
Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian…
We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the…
Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales,…
Uncovering human mobility patterns is of fundamental importance to the understanding of epidemic spreading, urban transportation and other socioeconomic dynamics embodying spatiality and human travel. According to the direct travel diaries…
Animal movements have been related to optimal foraging strategies where self-similar trajectories are central. Most of the experimental studies done so far have focused mainly on fitting statistical models to data in order to test for…
Recent advances in human mobility research have revealed consistent pairwise characteristics in movement behavior, yet existing mobility models often overlook the spatial and topological structure of mobility networks. By analyzing millions…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
Animals foraging alone are hypothesized to optimize the encounter rates with resources through L\'evy walks. However, the issue of how the interactions between multiple foragers influence their search efficiency is still not completely…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of…
Multiple-scale mobility is ubiquitous in nature and has become instrumental for understanding and modeling animal foraging behavior. However, the impact of individual movements on the long-term stability of populations remains largely…
We study analytically a simple random walk model on a one-dimensional lattice, where at each time step the walker resets to the maximum of the already visited positions (to the rightmost visited site) with a probability $r$, and with…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
It is highly believed that the individuals' mobility plays an important role in phase transition in animal collective motion. Here, we propose a model to study the effects of individuals' mobility in a distributed animal collective…
We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behaviour have aimed to understand how a globally ordered state may emerge from simple…