Advancements in Stochastic Processes and Random Matrices

Dear Colleagues,

Stochastic processes are ubiquitous in the real world, where uncertainty is an important factor. They have significant implications in economics, biology, physics, and mathematics, as they exhibit probabilistic behavior over time, offering robust frameworks for modeling complex systems where uncertainty plays a pivotal role.

Closely linked to stochastic processes is random matrix theory, which can be seen as a high-dimensional extension of these processes. Originally developed to analyze heavy atoms, random matrix theory has since expanded its scope, with recent developments uncovering deep connections to number theory, statistical mechanics, solid-state physics, and the dynamics of complex networks. These advancements highlight the versatility of random matrix theory in addressing problems across diverse fields.

This Special Issue will highlight cutting-edge research that bridges theory and application, building on the synergies between stochastic processes and random matrix theory. Contributions may range from innovative theoretical models designed to explain real-world complex phenomena to algorithms for analyzing high-dimensional data using stochastic techniques and novel applications in quantum physics and disordered systems, where random matrix models elucidate transition states and phase changes. By showcasing interdisciplinary approaches and real-world applications, we aim to inspire researchers to further explore the connections between these two vibrant areas of study through diverse models.

Together, the articles in this issue will not only deepen our understanding of mathematical theories but also shed light on their practical implications, paving the way for future innovations in both academic and applied contexts. This Special Issue encourages the presentation of enhanced techniques that explore the interplay between randomness and hidden structures in the system, emphasizing the transformative potential of combining stochastic processes and random matrix theory.

Prof. Dr. Manuel O Cáceres
Dr. Marco Nizama
Guest Editors

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• statistical mechanics on random planar graphs
• disorder in classic and quantum systems
• stochastic and active random media
• data science and machine learning
• information theory
• number theory
• non-equilibrium physics
• complex chemistry
• biology models
• economic sciences
• social sciences