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We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We study the collective dynamics of repulsive self-propelled particles. The particles are governed by coupled equations of motion that include polar self-propulsion, damping of velocity and of polarity, repulsive particle-particle…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
Chaotic behavior of quantum systems can be characterized by the adherence of the expectation values of given probes to moments of the Haar distribution. In this work, we analyze the behavior of several probes of chaos using a technique…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful…
Active matter deals with systems whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures several models have been suggested, such as the on-lattice model of…
We study analytically how noninteracting weakly active particles, for which passive Brownian diffusion cannot be neglected and activity can be treated perturbatively, distribute and behave near boundaries in various geometries. In…
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…
We study the Gaussian hermitian random matrix ensemble with an external matrix which has an arbitrary number of eigenvalues with arbitrary multiplicity. We compute the limiting eigenvalues correlations when the size of the matrix goes to…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
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…
The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e.,…
Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…
We study the off-diagonal matrix elements of observables that break the translational symmetry of a spin-chain Hamiltonian, and as such connect energy eigenstates from different total quasimomentum sectors. We consider quantum-chaotic and…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…
We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is…