Random Matrix Theory and Its Innovative Applications
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".
Deadline for manuscript submissions: 31 August 2024 | Viewed by 248
Special Issue Editors
Interests: nonequilibrium statistical mechanics; phase transitions and critical phenomena; stochastic aspects of game theory; modeling of social and economic systems; Monte Carlo simulations; random matrices theory; stochastic modeling of RTS noise in semiconductor devices
Special Issue Information
Dear Colleagues,
Spectral properties serve as fundamental tools in physics, with random matrices playing a pivotal role in understanding complex phenomena. Random matrices, characterized by entries chosen according to specific probability distributions, have gained prominence in various scientific applications.
In the 1950s, Eugene Wigner proposed an innovative approach to describe the spectra of heavy nuclei using Hermitian matrices. His simpler proposal, involving symmetric matrices with randomly chosen elements from a specific distribution, led to the emergence of the semi-circle law, describing the density of eigenvalues.
Subsequent work by Dyson and Metha established that the predictions of the random matrices theory provide an average across all possible interactions. These predictions, deemed universal, extend to diverse systems, encompassing not only the density of eigenvalues but also the distribution of eigenvalue spacings. Universal laws persist across different classes of random matrices, including correlation random matrices derived from uncorrelated time series, as observed in the well-known Wishart ensembles.
However, deviations from these universal laws hold significance, serving as indicators of peculiarities within various physics models. Notably, such deviations may signify the presence of phase transitions and critical phenomena in diverse contexts.
This Special Issue seeks original contributions in the realm of random matrices, encouraging theoretical explorations and practical applications in physics, econophysics, and other complex systems. Authors are invited to delve into the nuanced interplay of universal laws and deviations, shedding light on the broader implications of understanding intricate physical and economic phenomena.
Prof. Dr. Roberto Da Silva
Dr. Prado Sandra Denise
Guest Editors
Manuscript Submission Information
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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.
Keywords
- random matrices
- deviations from universal laws
- phase transitions and critical phenomena
