Related papers: Hydrodynamical spectral evolution for random matri…
We solve a family of Gaussian two-matrix models with rectangular Nx(N+v) matrices, having real asymmetric matrix elements and depending on a non-Hermiticity parameter mu. Our model can be thought of as the chiral extension of the real…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation arising to characterize the limit spectral measure of the…
In this paper, we consider tridiagonal matrices the eigenvalues of which evolve according to $\beta$-Dyson Brownian motion. This is the stochastic gradient flow on $\mathbb{R}^n$ given by, for all $1 \leq i \leq n,$ \[ d\lambda_{i,t} =…
We propose an integrable discrete model of one-dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection-diffusion equation with a nonlinear flux…
The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of…
We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave…
In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real $(\beta = 1)$, complex ($\beta = 2)$ and real…
This article considers some classes of models dealing with the dynamics of discrete curves subjected to stochastic deformations. It turns out that the problems of interest can be set in terms of interacting exclusion processes, the ultimate…
Under appropriate conditions for the initial configuration, the empirical measure of the $N$-particle Dyson model with parameter $\beta \geq 1$ converges to a unique measure-valued process as $N$ goes to infinity, which is independent of…
Some nonequilibrium systems exhibit anomalous suppression of the large-scale density fluctuations, so-called hyperuniformity. Recently, hyperuniformity was found numerically in a simple model of chiral active fluids [Q.-L. Lei et al., Sci.…
We give a sufficient condition under which the time-marginal law of $\mu$-reversible infinite interacting Brownian motions is characterised as the steepest gradient descent of the relative entropy in the Wasserstein space in the sense of…
A system of one-dimensional Brownian motions (BMs) conditioned never to collide with each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of hermitian matrix-valued diffusion process in the Gaussian unitary…
Since the introduction of Dyson's Brownian motion in early 1960's, there have been a lot of developments in the investigation of stochastic processes on the space of Hermitian matrices. Their properties, especially, the properties of their…
We study the asymptotic behavior of the eigenvalues of Gaussian perturbations of large Hermitian random matrices for which the limiting eigenvalue density vanishes at a singular interior point or vanishes faster than a square root at a…
We consider the hydrodynamic scaling behavior of the mass density with respect to a general class of mass conservative interacting particle systems on ${\mathbb Z}^n$, where the jump rates are asymmetric and long-range of order…
We investigate the process of eigenvalues of a symmetric matrix-valued process which upper diagonal entries are independent one-dimensional H\"older continuous Gaussian processes of order gamma in (1/2,1). Using the stochastic calculus with…
The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…
In this work, we prove a version of H\"{o}rmander's theorem for a stochastic evolution equation driven by a trace-class fractional Brownian motion with Hurst exponent $\frac{1}{2} < H < 1$ and an analytic semigroup on a given separable…
We obtain Fisher-Hartwig asymptotics with root and jump type singularities in space-time under the law of the stationary Hermitian Ornstein-Uhlenbeck process, which serve as a dynamical generalization of earlier static results obtained by…