Related papers: A simple hypocoercivity analysis for the effective…
We study measurement-induced nonlinear dynamics generated by an iterated quantum protocol combining an entangling gate, a single-qubit rotation, and post-selection. For pure single-qubit inputs, a particular choice of the single-qubit…
This paper introduces a geometric method for proving ergodicity of degenerate noise driven stochastic processes. The driving noise is assumed to be an arbitrary Levy process with non-degenerate diffusion component (but that may be applied…
In this work, we establish $\mathrm{L}^2$-exponential convergence for a broad class of Piecewise Deterministic Markov Processes recently proposed in the context of Markov Process Monte Carlo methods and covering in particular the Randomized…
We present a simple new proof for the stochastic homogenization of quasiconvex (level-set convex) Hamilton-Jacobi equations set in stationary ergodic environments. Our approach, which is new even in the convex case, yields more information…
We study stochastic model reduction for evolution equations in infinite dimensional Hilbert spaces, and show the convergence to the reduced equations via abstract results of Wong-Zakai type for stochastic equations driven by a scaled…
We study the ergodic properties of Schr\"odinger operators on a compact connected Riemannian manifold $M$ without boundary in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an…
We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…
Based on the Heisenberg-picture analog of the master equation, we develop a method for computing the exact time dependence of noise-averaged observables for general noninteracting fermionic systems with noisy fluctuations. Upon noise…
We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be unimodular, so an invariant measure may not exist. Ergodic…
K. It\^{o} characterised in \cite{ito} zero-mean stationary Gauss Markov-processes evolving on a class of infinite-dimensional spaces. In this work we extend the work of It\^{o} in the case of Hilbert spaces: Gauss-Markov families that are…
In this work we provide performance guarantees for hypocoercive non-reversible MCMC samplers $X_t$ with invariant measure $\mu_*$; our results apply in particular to the Langevin equation, Hamiltonian Monte-Carlo, and the bouncy particle…
Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…
In this article, we consider the weighted ergodic optimization problem of a class of dynamical systems $T:X\to X$ where $X$ is a compact metric space and $T$ is Lipschitz continuous. We show that once $T:X\to X$ satisfies both the {\em…
We propose a new model for approximating spatiotemporal noise covariance for use in MEG/EEG source analysis. Our model is an extension of an existing model [1,2] that uses a single Kronecker product of a pair of matrices - temporal and…
We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed in Refs. [Par1,Par2]. We apply our result to show that the…
Periodic measures are the time-periodic counterpart to invariant measures for dynamical systems and can be used to characterise the long-term periodic behaviour of stochastic systems. This paper gives sufficient conditions for the…
We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov-Fokker-Planck type of kinetic mean-field equation from the corresponding…
Dynamical systems that are contracting on a subspace are said to be semicontracting. Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical flow systems such as Markov chains. To develop a comprehensive…
We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau--Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain…
One proves in this work that the nonlinear semigroup $S(t)$ in $L^1(\mathbb R^d)$, $d\geq 3$, associated with the nonlinear Fokker-Planck equation $u_t-\Delta\beta(u)+\text{div}(Db(u)u){=}0$, $u(0)=u_0$ in $(0,\infty)\times\mathbb R^d$,…