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The dynamic spatial redistribution of individuals is a key driving force of various spatiotemporal phenomena on geographical scales. It can synchronise populations of interacting species, stabilise them, and diversify gene pools [1-3].…
The metaverse promises a shift in the way humans interact with each other, and with their digital and physical environments. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws…
Quantifying space exploration is a central question in random walk theory, with direct applications ranging from animal foraging, diffusion-limited reactions, and intracellular transport to stock markets. In particular, the explored domain…
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…
Probability distributions of human displacements has been fit with exponentially truncated L\'evy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the…
Urban scaling and Zipf's law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about…
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…
Trip distribution laws are basic for the travel demand characterization needed in transport and urban planning. Several approaches have been considered in the last years. One of them is the so-called gravity law, in which the number of…
Human mobility has been empirically observed to exhibit Levy flight characteristics and behaviour with power-law distributed jump size. The fundamental mechanisms behind this behaviour has not yet been fully explained. In this paper, we…
We study a random walk model in which the jumping probability to a site is dependent on the number of previous visits to the site, as a model of the mobility with memory. To this end we introduce two parameters called the memory parameter…
We introduce a simple and generic model that reproduces Zipf's law. By regarding the time evolution of the model as a random walk in the logarithmic scale, we explain theoretically why this model reproduces Zipf's law. The explanation shows…
Predicting human mobility patterns has many practical applications in urban planning, traffic engineering, infectious disease epidemiology, emergency management and location-based services. Developing a universal model capable of accurately…
Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to anyarbitrary region, and the fluxes between any two regions. The considered description offers a general and unified…
The study of human mobility patterns is a crucially important research field for its impact on several socio-economic aspects and, in particular, the measure of regularity patters of human mobility can provide a across-the-board view of…
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
Understanding the patterns of mobility of individuals is crucial for a number of reasons, from city planning to disaster management. There are two common ways of quantifying the amount of travel between locations: by direct observations…
The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws, that can be derived from experimental data averaged in time or space,assuming the system in a steady state. One of the major…
Human mobility is a fundamental aspect of social behavior, with broad applications in transportation, urban planning, and epidemic modeling. Represented by the gravity model and the radiation model, established analytical models for…
The recent availability of digital traces from Information and Communications Technologies (ICT) has facilitated the study of both individual- and population-level movement with unprecedented spatiotemporal resolution, enabling us to better…
Although a number of studies have investigated human mobility patterns during natural hazards, mechanistic models that capture mobility dynamics under large-scale perturbations, such as extreme floods, remain scarce. Leveraging mobile phone…