相关论文: Random matrix ensemble for the covariance matrix o…

We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…

The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an $O(N)$ Bayesian method to estimate the drift and diffusion…

Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…

The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those…

We study the RPA equations in their most general form by taking the matrix elements appearing in the RPA equations as random. This yields either a unitarily or an orthogonally invariant random-matrix model which is not of the Cartan type.…

We propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with Markov processes on graphs. We argue that the spectral statistics of such an ensemble (after ensemble averaging) depends…

This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…

In these notes I explain how to describe one-dimensional quantum systems that are simultaneously near to, but not exactly at, a critical point, and in a far-from-equilibrium steady state. This description uses a density matrix on scattering…

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

In this paper we show that the empirical eigenvalue distribution of any sample covariance matrix generated by independent copies of a stationary regular sequence has a limiting distribution depending only on the spectral density of the…

We study the density of states measure for some class of random unitary band matrices and prove a Thouless formula relating it to the associated Lyapunov exponent. This class of random matrices appears in the study of the dynamical…

Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails,…

We consider a system of linear oscillators, or quantum states, described by Random Matrix Theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak…

We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N…

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of…

We study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein-Uhlenbeck process. We also consider an…

A theoretical description of quantum mechanical steady states is developed. Applications for simple quantum mechanical systems described in terms of coupled level structures yield a formulation equivalent to time independent scattering…

We study the asymptotic stability for large times of homogeneous stationary states for the nonlinear Hartree equation for density matrices in Rd for d\geq3. We can reach both the optimal Sobolev and Schatten exponents for the initial data,…

This paper proposes a stochastic approach to model temperature dynamic and study related risk measures. The dynamic of temperatures can be modelled by a mean-reverting process such as an Ornstein-Uhlenbeck one. In this study, we estimate…