Related papers: Hitting statistics for $\phi$-mixing dynamical sys…
We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases:…
Hybrid dynamical systems are systems which posses both continuous and discrete transitions. Assuming that the discrete transitions (resets) occur a finite number of times, the optimal control problem can be solved by gluing together the…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
We start by reviewing recent probabilistic results on ergodic sums in a large class of (non-uniformly) hyperbolic dynamical systems. Namely, we describe the central limit theorem, the almost-sure convergence to the gaussian and other stable…
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…
Symmetry imposes constraints on open quantum systems, affecting the dissipative properties in nonequilibrium processes. Superradiance is a typical example in which the decay rate of the system is enhanced via a collective system-bath…
A novel representation of reset control systems with a zero-crossing resetting law, in the framework of hybrid inclusions, is postulated. The problems of well-posedness and stability of the resulting hybrid dynamical system are…
The mixer chain on a graph G is the following Markov chain. Place tiles on the vertices of G, each tile labeled by its corresponding vertex. A "mixer" moves randomly on the graph, at each step either moving to a randomly chosen neighbor, or…
We present an adaptation of Stein's method of normal approximation to the study of both discrete- and continuous-time dynamical systems. We obtain new correlation-decay conditions on dynamical systems for a multivariate central limit…
We show that for non-degenerate $k$-Markovian random fields with finite state space over a bounded degree graph with exponential growth rate $\theta$ uniform $\phi$-mixing with exponential decay rate $\lambda > 3\theta$ implies uniform…
Two different dynamical system formulations are presented for the generic $f(R,\phi,X)$ family of gravity theories. As illustrative examples, the first and the second formulation is applied to study the phase space of a toy model of the…
We prove an upper bound on the total variation mixing time of a finite Markov chain in terms of the absolute spectral gap and the number of elements in the state space. Unlike results requiring reversibility or irreducibility, this bound is…
Consider Glauber dynamics for the Ising model on a graph of $n$ vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least $n\log n/f(\Delta)$, where $\Delta$ is the maximum degree and $f(\Delta) = \Theta(\Delta…
We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in…
Dynamic arrest is a general phenomenon across a wide range of dynamic systems, but the universality of dynamic arrest phenomena remains unclear. We relate the emergence of traffic jams in a simple traffic flow model to the dynamic slow down…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
A fundamental problem of non-equilibrium statistical mechanics is the derivation of macroscopic transport equations in the hydrodynamic limit. The rigorous study of such limits requires detailed information about rates of convergence to…
We establish tight results for rapid mixing of Gibbs samplers for the Ferromagnetic Ising model on general graphs. We show that if \[(d-1)\tanh\beta<1,\] then there exists a constant C such that the discrete time mixing time of Gibbs…
We prove that a Gibbs point process interacting via a finite-range, repulsive potential $\phi$ exhibits a strong spatial mixing property for activities $\lambda < e/\Delta_{\phi}$, where $\Delta_{\phi}$ is the potential-weighted connective…