The standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat principle (rays) and the Huygens principle (wavefronts), we formulate the Hamilton-Jacobi dynamics for large random matrix models. The resulting equations describe a broad class of random matrix models in a unified way, including normal (Hermitian or unitary) as well as strictly non-normal dynamics. This formalism applied to Brownian bridge dynamics allows one to calculate the asymptotics of the Harish-Chandra-Itzykson-Zuber integrals.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.104.054111 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Allocation Predictability of Individual Assignments in Restricted Randomization Designs for Two-Arm Equal Allocation Trials.
Stat Med
February 2025
Medical University of South Carolina, Charleston, South Carolina, USA.
This manuscript derives the allocation predictability measured by the correct guess probability and the probability of being deterministic for individual treatment assignments, as well as the averages of a randomization sequence, based on the treatment imbalance transition matrix and the conditional allocation probability. The methods described are applicable to restricted randomization designs that satisfy the following criteria: (1) two-arm equal allocation, (2) restriction of maximum tolerated imbalance, and (3) conditional allocation probability fully determined by the observed current treatment imbalance. Analytical results indicate that, for two-arm equal allocation trials, allocation predictability alternates by the odd/even sequence order of the treatment assignment.
View Article and Find Full Text PDFBovine dairy products and flow mediated dilation (FMD): a systematic review of the published evidence.
Eur J Nutr
January 2025
Food for Health Ireland, University College Dublin, Dublin 4, Republic of Ireland.
Purpose: Evidence suggests bovine dairy products may have neutral or beneficial effects on cardiometabolic health, despite being a source of saturated fat. The dairy matrix, the structure and combination of protein, fat, and other nutrients, and how they interact with each other, is purported to be responsible for these beneficial health effects. Whether this relationship extends to endothelial function, as assessed by flow mediated dilation (FMD), remains to be elucidated.
View Article and Find Full Text PDFHypoxia-Inducible Factor Prolyl Hydroxylase Inhibitor Roxadustat Accelerates Wound Healing in a Mouse Hind limb Lymphedema Model.
Adv Wound Care (New Rochelle)
January 2025
Department of Plastic and Reconstructive Surgery, Faculty of Medicine and Graduate School of Medicine, Hokkaido University, Sapporo, Japan.
Drugs regulating hypoxia-inducible factor (HIF)-1α have not been investigated for wound healing in lymphedema. Therefore, we examined the effects of drug modulation of HIF-1α activity for wound healing in our previously developed mouse model of nonirradiated hind limb lymphedema. Mouse hind limb lymphedema models ( = 17) and a sham group ( = 6) were created using 8- to 10-week-old male C57BL/6N mice.
View Article and Find Full Text PDFBatch Adsorption of Orange II Dye on a New Green Hydrogel-Study on Working Parameters and Process Enhancement.
Gels
January 2025
Ecole Nationale Supérieure de Chimie de Rennes, Univ. Rennes, CNRS, UMR 6226, CEDEX 7, 35708 Rennes, France.
A new green hydrogel consisting of cherry stone (CS) powder and sodium alginate (SA) was synthesized through physical crosslinking. The product had a mean diameter of 3.95 mm, a moisture content of 92.
View Article and Find Full Text PDFQuadratic Forms in Random Matrices with Applications in Spectrum Sensing.
Entropy (Basel)
January 2025
Department of Electronics and Telecommunications (DET), Politecnico di Torino, 10129 Turin, Italy.
Quadratic forms with random kernel matrices are ubiquitous in applications of multivariate statistics, ranging from signal processing to time series analysis, biomedical systems design, wireless communications performance analysis, and other fields. Their statistical characterization is crucial to both design guideline formulation and efficient computation of performance indices. To this end, random matrix theory can be successfully exploited.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!