Related papers: Circular Rosenzweig-Porter random matrix ensemble
We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is white-in-time and spatial homogeneous and isotropic. We will show that in the…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…
As written by statistician George Box "All models are wrong, but some are useful", standard diffusion derivation or Feynman path ensembles use nonphysical infinite velocity/kinetic energy nowhere differentiable trajectories - what seems…
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The…
A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…
We consider the influence of active speed fluctuations on the dynamics of a $d$-dimensional active Brownian particle performing a persistent stochastic motion. We use the Laplace transform of the Fokker-Planck equation to obtain exact…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
Generic rotationally invariant random matrix models satisfy a simple relation: the probability distribution of off-diagonal elements and the one of half the difference between any two diagonal elements coincide. In the spirit of the…
We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread…
A random matrix ensemble incorporating both GUE and Poisson level statistics while respecting $U(N)$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one dimensional fermions at finite temperature.
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
Two families of stochastic interacting particle systems, the interacting Brownian motions and Bessel processes, are defined as extensions of Dyson's Brownian motion models and the eigenvalue processes of the Wishart and Laguerre processes…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We study the effect of highly oscillatory potentials to the eigenvalues of a random matrix. Consider the circular unitary ensembles with an external potential which is periodic with the period comparable to the average spacing of the…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
We endow the elements of a random matrix drawn from the Gaussian Unitary Ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the…
We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the…
Matrix models showing chaotic-integrable transition in the spectral statistics are important for understanding Many Body Localization (MBL) in physical systems. One such example is the $\beta$-ensemble, known for its structural simplicity.…
We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation…