Related papers: Sharp spectral gap of adaptive Langevin dynamics

We consider Fokker-Planck type differential operators associated with general Langevin processes admitting a Gibbs stationary distribution. Under assumptions insuring suitable resolvent estimates, we prove Eyring-Kramers formulas for the…

We consider Kramers-Fokker-Planck operators with general degenerate coefficients. We prove semiclassical hypocoercivity estimates for a large class of such operators. Then, we manage to prove Eyring-Kramers formulas for the bottom of the…

We consider Witten Laplacians associated to some non-Morse potentials. We prove Eyring-Kramers formulas for the bottom of the spectrum of these operators in the semiclassical regime and quantify the spectral gap separating these eigenvalues…

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…

We consider higher-derivative perturbations of quantum gravity and quantum field theories in curved space and investigate tools to calculate counterterms and short-distance expansions of Feynman diagrams. In the case of single…

We present the quantitative method of the recent work arXiv:2209.09340 in a simple setting, together with a compactness argument that was not included in arXiv:2209.09340 and has interest per se. We are concerned with the exponential…

We derive novel low-temperature asymptotics for the spectrum of the infinitesimal generator of the overdamped Langevin dynamics. The novelty is that this operator is endowed with homogeneous Dirichlet conditions at the boundary of a domain…

We prove the consistency of Galerkin methods to solve Poisson equations where the differential operator under consideration is the generator of the Langevin dynamics. We show in particular how the hypocoercive nature of this operator can be…

We introduce a variational formulation for a general class of possibly degenerate, non-self-adjoint Fokker-Planck operators in divergence form, motivated by the work of Albritton et al. (2024), and prove that it is suitable for defining the…

In this paper, we present a spectral optimal control framework for Fokker-Planck equations based on the standard ground state transformation that maps the Fokker-Planck operator to a Schrodinger operator. Our primary objective is to…

Adaptive Langevin dynamics is a method for sampling the Boltzmann-Gibbs distribution at prescribed temperature in cases where the potential gradient is subject to stochastic perturbation of unknown magnitude. The method replaces the…

Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…

We consider the problem of building a continuous stochastic model, i.e. a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom…

The goal of this work is to find the sharp rate of convergence to equilibrium under the quadratic Fisher information functional for solutions to Fokker-Planck equations governed by a constant drift term and a constant, yet possibly…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Nonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time. Learning the Koopman operator and its spectral decomposition from data is enabled…

Starting from a forward--backward path integral of a point particle in a bath of harmonic oscillators, we derive the Fokker-Planck and Langevin equations with and without inertia. Special emphasis is placed upon the correct operator order…

We investigate the existence of steady states and exponential decay for hypocoercive Fokker--Planck equations on the whole space with drift terms that are linear in the position variable. For this class of equations, we first establish that…

An improved method for driving a system into a desired distribution, for example, the Gibbs-Boltzmann distribution, is proposed, which makes use of an artificial relaxation process. The standard techniques for achieving the Gibbs-Boltzmann…

This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting…