Related papers: Dynamical Universality for Random Matrices
The random matrix ensembles (RME), especially Gaussian RME and Ginibre RME, are applied to nuclear systems, molecular systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). Measures of quantum chaos and quantum…
A well known conjecture of Wigner, Dyson, and Mehta asserts that the (appropriately normalized) $k$-point correlation functions of the eigenvalues of random $n \times n$ Wigner matrices in the bulk of the spectrum converge (in various…
Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their far-from-equilibrium dynamics and statistics…
Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's…
In this paper, we present a "stellar dynamics" model of an infinite Universe, where matter distribution follows an inverse proportionality squared relationship with respect to the distance from the rotation center of galaxy clusters and…
We address the dynamics of quantum correlations in continuous variable open systems and analyze the evolution of bipartite Gaussian states in independent noisy channels. In particular, upon introducing the notion of dynamical path through a…
In the past 20 years, the study of real eigenvalues of non-symmetric real random matrices has seen important progress. Notwithstanding, central questions still remain open, such as the characterization of their asymptotic statistics and the…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…
Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…
The G-Brownian-motion-driven stochastic differential equations (G-SDEs) as well as the G-expectation, which were seminally proposed by Peng and his colleagues, have been extensively applied to describing a particular kind of uncertainty…
Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…
Interacting random matrix systems are fundamental to modern theoretical physics and data science, yet a unified framework for their analysis has been lacking. This work introduces such a universal framework, built upon two novel concepts:…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
We establish sharp global rigidity upper bounds for universal determinantal point processes describing edge eigenvalues of random matrices. For this, we first obtain a general result which can be applied to general (not necessarily…
Universality is a powerful concept, which enables making qualitative and quantitative predictions in systems with extensively many degrees of freedom. It finds realizations in almost all branches of physics, including in the realm of…
A scalar-tensor theory of gravity is formulated in which $G$ and particle masses are allowed to vary. The theory yields a globally static cosmological model with no evolutionary timescales, no cosmological coincidences, and no flatness and…
A universal model for D=4 spinning particle is constructed with the configuration space chosen as ${\bf R}^{3,1}\times S^2$, where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible…
We consider statistical tasks in high dimensions whose loss depends on the data only through its projection into a fixed-dimensional subspace spanned by the parameter vectors and certain ground truth vectors. This includes classifying…