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This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

Probability · Mathematics 2026-04-28 Hubert Woszczek , Marek A. Teuerle , Agnieszka Wyłomańska

In this work we present a measurement study of user mobility in Second Life. We first discuss different techniques to collect user traces and then focus on results obtained using a crawler that we built. Tempted by the question whether our…

Computers and Society · Computer Science 2009-09-29 Chi-Anh La , Pietro Michiardi

From footpaths to flight routes, human mobility networks facilitate the spread of communicable diseases. Control and elimination efforts depend on characterizing these networks in terms of connections and flux rates of individuals between…

Populations and Evolution · Quantitative Biology 2016-01-29 Kyle B Gustafson , Basil S. Bayati , Philip A. Eckhoff

L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…

Statistical Mechanics · Physics 2019-03-27 Bartłomiej Dybiec , Karol Capała , Aleksei Chechkin , Ralf Metzler

Urbanization and its problems require an in-depth and comprehensive understanding of urban dynamics, especially the complex and diversified lifestyles in modern cities. Digitally acquired data can accurately capture complex human activity,…

Physics and Society · Physics 2022-09-27 Yanni Yang , Alex Pentland , Esteban Moro

Human mobility patterns are surprisingly structured. In spite of many hard to model factors, such as climate, culture, and socioeconomic opportunities, aggregate migration rates obey a universal, parameter-free, `radiation' model. Recent…

The empirical relation between density and velocity of pedestrian movement is not completely analyzed, particularly with regard to the `microscopic' causes which determine the relation at medium and high densities. The simplest system for…

Physics and Society · Physics 2009-11-11 Armin Seyfried , Bernhard Steffen , Wolfram Klingsch , Maik Boltes

The information collected by mobile phone operators can be considered as the most detailed information on human mobility across a large part of the population. The study of the dynamics of human mobility using the collected geolocations of…

Social and Information Networks · Computer Science 2013-11-21 Nicolas Ponieman , Alejo Salles , Carlos Sarraute

Mobility and network traffic have been traditionally studied separately. Their interaction is vital for generations of future mobile services and effective caching, but has not been studied in depth with real-world big data. In this paper,…

Networking and Internet Architecture · Computer Science 2018-11-07 Babak Alipour , Mimonah Al Qathrady , Ahmed Helmy

Social structures influence a variety of human behaviors including mobility patterns, but the extent to which one individual's movements can predict another's remains an open question. Further, latent information about an individual's…

Physics and Society · Physics 2022-04-27 Zexun Chen , Sean Kelty , Brooke Foucault Welles , James P. Bagrow , Ronaldo Menezes , Gourab Ghoshal

We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as…

Statistical Mechanics · Physics 2015-05-19 Ihor Lubashevsky , Andreas Heuer , Rudolf Friedrich , Ramil Usmanov

The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events…

Statistical Mechanics · Physics 2012-04-03 S. Denisov , V. Zaburdaev , P. Hanggi

Understanding and modeling human mobility is central to challenges in transport planning, sustainable urban design, and public health. Despite decades of effort, simulating individual mobility remains challenging because of its complex,…

Physics and Society · Physics 2026-02-10 Ye Hong , Yatao Zhang , Konrad Schindler , Martin Raubal

Pedestrian routing choices play a crucial role in shaping collective crowd dynamics, yet the influence of interactions among unfamiliar individuals remains poorly understood. In this study, we analyze real-world pedestrian behavior at a…

Physics and Society · Physics 2026-03-25 Ziqi Wang , Alessandro Gabbana , Federico Toschi

Human mobility describes physical patterns of movement of people within a spatial system. Many of these patterns, including daily commuting, are cyclic and quantifiable. These patterns capture physical phenomena tied to processes studied in…

Applications · Statistics 2023-01-10 Michael J. Kane , Owais Gilani , Simon Urbanek

The movement of pedestrians is supposed to show certain regularities which can be best described by an ``algorithm'' for the individual behavior and is easily simulated on computers. This behavior is assumed to be determined by an intended…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing

In this paper we focus on the problem of human activity recognition without identification of the individuals in a scene. We consider using Wi-Fi signals to detect certain human mobility behaviors such as stationary, walking, or running.…

Networking and Internet Architecture · Computer Science 2018-08-06 Fang-Jing Wu , Gürkan Solmaz

In empirical studies of random walks, continuous trajectories of animals or individuals are usually sampled over a finite number of points in space and time. It is however unclear how this partial observation affects the measured…

Physics and Society · Physics 2018-03-13 Riccardo Gallotti , Rémi Louf , Jean-Marc Luck , Marc Barthelemy

Principles of self-organization play an increasingly central role in models of human activity. Notably, individual human displacements exhibit strongly recurrent patterns that are characterized by scaling laws and can be mechanistically…

Neurons and Cognition · Quantitative Biology 2012-03-28 Denis Boyer , Margaret C. Crofoot , Peter D. Walsh

Predicting human displacements is crucial for addressing various societal challenges, including urban design, traffic congestion, epidemic management, and migration dynamics. While predictive models like deep learning and Markov models…

Computers and Society · Computer Science 2024-08-07 Sebastiano Bontorin , Simone Centellegher , Riccardo Gallotti , Luca Pappalardo , Bruno Lepri , Massimiliano Luca
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