Related papers: Hypocoercivity with Schur complements
We prove a semiclassical resolvent estimate for a broad class of non-self-adjoint, non-elliptic pseudodifferential operators in the low-lying spectral regime. The proof relies on improved ellipticity properties for the symbol of the…
We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are…
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based…
We refine the understanding of continuous dependence on coefficients of solution operators under the nonlocal $H$-topology viz Schur topology in the setting of evolutionary equations in the sense of Picard. We show that certain components…
This paper introduces a very fast method for the computation of the resolvent of fractional powers of operators. The analysis is kept in the continuous setting of (potentially unbounded) self adjoint positive operators in Hilbert spaces.…
Following on our previous work [S. Delong and B. E. Griffith and E. Vanden-Eijnden and A. Donev, Phys. Rev. E, 87(3):033302, 2013], we develop temporal integrators for solving Langevin stochastic differential equations that arise in…
In this note, we prove weighted resolvent estimates for the semiclassical Schr\"odinger operator $-h^2 \Delta + V(x) : L^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$, $n \neq 2$. The potential $V$ is real-valued, and assumed to either decay at…
The aim of this paper is to offer an original and comprehensive spectral theoretical approach to the study of convergence to equilibrium, and in particular of the hypocoercivity phenomenon, for contraction semigroups in Hilbert spaces. Our…
We study the linear relaxation Boltzmann equation, a simple semiclassical kinetic model. We provide a resolvent estimate for an associated non-selfadjoint operator as well as an estimate on the return to equilibrium. This is done using a…
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, by means of well-chosen Lyapunov functionals. Typical examples are the kinetic Fokker--Planck and Boltzmann…
In this note, we consider a kinetic Fokker-Planck-Alignment equation with Rayleigh-type friction and self-propulsion force which is derived from general environmental averaging models. We show the exponential relaxation in time toward…
We establish necessary and sufficient conditions for viability of evolution inclusions with locally monotone operators in the sense of Liu and R\"ockner [J. Funct. Anal., 259 (2010), pp. 2902-2922]. This allows us to prove wellposedness of…
We establish sharp boundary regularity results for solutions to kinetic Fokker-Planck equations under prescribed inflow boundary conditions, providing precise quantification of the boundary hypoelliptic regularization effect. For equations…
In this article we develop a new abstract strategy for proving ergodicity with explicit computable rate of convergence for diffusions associated with a degenerate Kolmogorov operator L. A crucial point is that the evolution operator L may…
We study the kinetic Fokker-Planck equation on the whole space with a confining potential. We show quantitative rates of exponential convergence to equilibrium in a well chosen Wasserstein-1 distance. We use the Wasserstein-1 version of…
This note provides a simple derivation of the overdamped approximation for kinetic (or underdamped) equilibrium Langevin dynamics, in cases where certain coefficients depend on the position variable. The equivalent small-mass limit of these…
We analyze infinite-dimensional non-linear degenerate stochastic differential equations with multiplicative noise. First, essential m-dissipativity of their associated Kolmogorov backward generators on $L^2(\mu^{\Phi})$ defined on smooth…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
This work establishes new results on spectral theory and time evolution for matrix-valued discrete Schr\"odinger operators on the space of square-summable matrix sequences. The matrix-valued formalism is employed to streamline notation,…
In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the…