Random Walks and Stochastic Processes in Complex Systems: From Physics to Socio-Economic Phenomena, Second Edition
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: 31 December 2025 | Viewed by 31
Special Issue Editors
2. Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Arhimedova 3, 1000 Skopje, Macedonia
3. Department of Physics, Korea University, Seoul 02841, Republic of Korea
Interests: statistical mechanics; mathematical physics; stochastic processes; anomalous diffusion; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Interests: fractional kinetics; fractional electrostatics; fractional quantum mechanics
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Random walks are underlying phenomena of various processes in nature, economics and social behavior. Theoretical investigations of random walks and stochastic processes in complex systems have been of great interest for years. Here, the modeling of random processes in complex systems, including complex networks and graphs, requires an interdisciplinary approach due to the different applications of the same, analogous, or similar models in various fields, such as physics, biology, computer science, economics and social sciences.
The vast amount of data obtained experimentally, observed empirically, and by means of computer simulations requires new theoretical approaches; that is, in order to understand the dynamics of the complex systems involved, this opening new avenues in physics, biology, computer science, engineering and economics. At present, methods of statistical physics have been applied to describe complex social phenomena using stochastic and kinetic differential equations and agent-based models. Analysis of the empirical data from various economic and financial systems has shown that, despite the abundance of proposed models, there is still a lack of models that accurately reproduce and explain the emergence of empirically observable statistical properties. One such example is the famed Ornstein–Uhlenbeck process, which has been used in physics to describe the random motion of a particle in a harmonic potential, but which can be also used to model interest and currency exchange rates. Furthermore, geometric Brownian motion, a universal model for self-reproducing phenomena, such as population and wealth, can also be used in mathematical finance (in the Black–Scholes model) for asset pricing, but also to model other natural phenomena such as bacterial cell division, and fragment sizes in rock crushing processes. It also relates to turbulent diffusion governed by inhomogeneous advection–diffusion equations. Moreover, the voter model is a part of sociophysics, and is used, for example, to model opinion dynamics. Different generalizations of the voter model, which can also be related to diffusion problems in physics, have also been introduced and applied to real data.
The purpose of this 2nd Edition of the Special Issue is to reflect the current situation in the application of random walks and stochastic models in various fields of science, such as physics, computer science, economics and social sciences. We kindly invite researchers working in these rapidly developing fields to contribute original research/review papers focusing on theoretical modeling and applications. We look forward to your contributions.
Dr. Trifce Sandev
Dr. Alexander Iomin
Guest Editors
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Keywords
- random walks
- stochastic equations
- kinetic equations
- diffusion
- geometric Brownian motion
- voter model
- econophysics
- sociophysics
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