相关论文: Quantitative exponential mixing for the randomized…

We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence…

We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…

In this paper, we prove that weak solutions of 3D stochastic primitive equations have exponential mixing property if the noise is sufficiently smooth and non-degenerate. With the help of uniqueness of strong solution of 3D stochastic…

We consider deterministic homogenization (convergence to a stochastic differential equation) for multiscale systems of the form \[ x_{k+1} = x_k + n^{-1} a_n(x_k,y_k) + n^{-1/2} b_n(x_k,y_k), \quad y_{k+1} = T_n y_k, \] where the fast…

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that, if the Lebesgue measure of the set of points failing the non-uniform expansion or the slow recurrence to the…

We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and…

We show a strict hierarchy among various edge and vertex expansion properties of Markov chains. This gives easy proofs of a range of bounds, both classical and new, on chi-square distance, spectral gap and mixing time. The 2-gradient is…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

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…

We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd \times E where E is a finite set. The continuous component evolves according to a smooth vector field that…

In this short note we provide an elementary proof that a certain type of nonuniform sequential Doeblin minorization condition implies non-uniform sequential "geometric" ergodicity. Using this result several limit theorems for inhomogeneous…

For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous…

After a brief historical review of ergodicity and mixing in dynamics, particularly in quantum dynamics, we introduce definitions of quantum ergodicity and mixing using the structure of the system's energy levels and spacings. Our…

A central challenge in quantum physics is to understand the structural properties of many-body systems, both in equilibrium and out of equilibrium. For classical systems, we have a unified perspective which connects structural properties of…

In the context of stationary $\mathbb{Z}^d$ nearest-neighbour Gibbs measures $\mu$ satisfying strong spatial mixing, we present a new combinatorial condition (the topological strong spatial mixing property (TSSM)) on the support of $\mu$…

The paper provides a systematic characterization of quantum ergodic and mixing channels in finite dimensions and a discussion of their structural properties. In particular, we discuss ergodicity in the general case where the fixed point of…

In this paper, several fundamental facts, especially the existence and uniqueness of an absolutely continuous ergodic measure with an exponential mixing rate, are derived for smooth expanding circle maps. Although the results are classical,…

We study one-dimensional lattice systems with pair-wise interactions of infinite range. We show projective convergence of Markov measures to the unique equilibrium state. For this purpose we impose a slightly stronger condition than…

In this short note we prove ``effective" geometric ergodicity (i.e a Perron-Frobenius theorem) for Markov chains in random mixing dynamical environment satisfying a random non-uniform version of the Doeblin condition. Effectivity here means…

For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…