Related papers: Edge Behavior of Higher Complex-Dimensional Determ…
The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. P05014 (2012)] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates…
We introduce a generalized $d$-dimensional Fermi-Pasta-Ulam (FPU) model in presence of long-range interactions, and perform a first-principle study of its chaos for $d=1,2,3$ through large-scale numerical simulations. The nonlinear…
The emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing. In this paper, we develop a computational technique using distributed processing elements in a complex network,…
Recently we introduced a family of $U(N)$ invariant Random Matrix Ensembles which is characterized by a parameter $\lambda$ describing logarithmic soft-confinement potentials $V(H) \sim [\ln H]^{(1+\lambda)} \:(\lambda>0$). We showed that…
Akemann, Ipsen and Kieburg recently showed that the squared singular values of products of M rectangular random matrices with independent complex Gaussian entries are distributed according to a determinantal point process with a correlation…
We have discussed earlier the correlation functions of the random variables $\det(\la-X)$ in which $X$ is a random matrix. In particular the moments of the distribution of these random variables are universal functions, when measured in the…
We investigate the overlap matrix between the eigenvectors of a Wigner matrix $H_{N+K}$ of size $(N+K)\times(N+K)$ and those of its principal minor $H_N$ of size $N\times N$, for both the real symmetric ($\beta=1$) and complex Hermitian…
Using field theoretic renormalization group methods we study the critical behavior of a driven diffusive system near a boundary perpendicular to the driving force. The boundary acts as a particle reservoir which is necessary to maintain the…
In this paper the kernel for the spectral correlation functions of the invariant chiral random matrix ensembles with real ($\beta =1$) and quaternion real ($\beta = 4$) matrix elements is expressed in terms of the kernel of the…
Consider the random matrix model $A^{1/2} UBU^* A^{1/2},$ where $A$ and $B$ are two $N \times N$ deterministic matrices and $U$ is either an $N \times N$ Haar unitary or orthogonal random matrix. It is well-known that on the macroscopic…
While modern representation learning relies heavily on global error signals, decentralized algorithms driven by local interactions offer a fundamental distributed alternative. However, the macroscopic convergence properties of these…
Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which…
Generative models have proven to be an outstanding tool for representing high-dimensional probability distributions and generating realistic-looking images. An essential characteristic of generative models is their ability to produce…
Given a relatively compact set $\Omega \subseteq \mathbb{R}$ of Lebesgue measure $|\Omega|$ and $\varepsilon > 0$, we show the existence of a set $\Lambda \subseteq \mathbb{R}$ of uniform density $D (\Lambda) \leq (1+\varepsilon) |\Omega|$…
We develop a generalized gradient expansion of the inhomogeneous dynamical mean-field theory method for determining properties of ultracold atoms in a trap. This approach goes beyond the well-known local density approximation and at higher…
We prove that the spectral radius of a large random matrix $X$ with independent, identically distributed complex entries follows the Gumbel law irrespective of the distribution of the matrix elements. This solves a long-standing conjecture…
SDE-based methods such as denoising diffusion probabilistic models (DDPMs) have shown remarkable success in real-world sample generation tasks. Prior analyses of DDPMs have been focused on the exponential Euler discretization, showing…
This paper proposes a new pattern of two dimensional cellular automata linear rules that are used for efficient edge detection of an image. Since cellular automata is inherently parallel in nature, it has produced desired output within a…
The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be generally improved either by increasing the number of training points or by improving the…
We consider the complex Elliptic Ginibre Ensemble, a family of random matrix models introduced by Girko that interpolates between the Ginibre Ensemble and the Gaussian Unitary Ensemble and such that its empirical spectral measure converges…