Random Walks and Stochastic Processes in Complex Systems: From Physics to Socio-Economic Phenomena

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. The modeling of random processes in complex systems, including complex networks and graphs, requires an interdisciplinary approach due to the different applications of 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 or observed empirically and by means of computer simulations requires new theoretical approaches in order to understand the dynamics of such complex systems, which open new vistas in physics, biology, computer science, engineering and economics. Nowadays, methods of statistical physics have been applied to describe complex social phenomena using stochastic and kinetic differential equations or 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 can be also used to model interest and currency exchange rates. Furthermore, geometric Brownian motion, which is an 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, fragment sizes in rock crushing processes, as well as being connected to turbulent diffusion governed by inhomogeneous advection–diffusion equations. Moreover, the voter model is a part of the area of sociophysics, and is used, for example, to model opinion dynamics. Different generalizations of the voter model, which can also be related to the diffusion problems in physics, have been introduced and applied to real data, as well.

The purpose of this 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 fields to contribute with original research/review papers dedicated to theoretical modeling and applications.

Dr. Trifce Sandev
Dr. Alexander Iomin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.