Related papers: Matrix models and growth processes: from viscous f…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
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 use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
We study a quantum system of $p$ commuting matrices and find that such a quantum system requires an explicit curvature dependent potential in its Lagrangian for the system to have a finite energy ground state. In contrast it is possible to…
We define a class of random matrix ensembles that pertain to random looped polymers. Such random looped polymers are a possible model for bio-polymers such as chromatin in the cell nucleus. It is shown that the distribution of the largest…
We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies…
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams…
In the first part of the talk, I review the applications of loop equations to the matrix models and to 2-dimensional quantum gravity which is defined as their continuum limit. The results concerning multi-loop correlators for low genera and…
In these lecture notes prepared for the 11th Taiwan Spring School, Taipei 1997}, and updated for the Saalburg summer school 1998, we review the solutions of O(N) or U(N) models in the large N limit and as 1/N expansions, in the case of…
Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to…
In this work, we study a class of random matrices which interpolate between the Wigner matrix model and various types of patterned random matrices such as random Toeplitz, Hankel, and circulant matrices. The interpolation mechanism is…
It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical…
Algorithms for learning distributions over weight-vectors, such as AROW were recently shown empirically to achieve state-of-the-art performance at various problems, with strong theoretical guaranties. Extending these algorithms to matrix…
In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most…