Related papers: THE CONVERGENCE OF CHAOTIC INTEGRALS
A general synthetic iterative scheme is proposed to solve the Enskog equation within a Monte Carlo framework. The method demonstrates rapid convergence by reducing intermediate Monte Carlo evolution and preserves the asymptotic-preserving…
We review the local Monte Carlo dynamics and Swendsen-Wang cluster algorithm. We introduce and analyze a new Monte Carlo dynamics known as transitional Monte Carlo. The transitional Monte Carlo algorithm samples energy probability…
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic…
Time derivatives of scalar fields occur quadratically in textbook actions. A simple Legendre transformation turns the lagrangian into a hamiltonian that is quadratic in the momenta. The path integral over the momenta is gaussian. Mean…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
We discuss Hamiltonian Monte Carlo (HMC) and event-chain Monte Carlo (ECMC) for the one-dimensional chain of particles with harmonic interactions and benchmark them against local reversible Metropolis algorithms. While HMC achieves…
It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the…
In this paper, a method to exactly sample the trajectories of inverse subordinators (in the sense of the finite-dimensional distributions), jointly with the undershooting or overshooting process, is provided. The method applies to general…
A new diagrammatic quantum Monte Carlo approach is proposed to deal with the imaginary time propagator involving both dynamic disorder (i.e., electron-phonon interactions) and static disorder of local or nonlocal nature in a unified and…
We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained.…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…
In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis.…
By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$, and the Reynolds number $Re$ is measured using direct…
We present a numerical algorithm for the computation of invariant Ruelle distributions on convex co-compact hyperbolic surfaces. This is achieved by exploiting the connection between invariant Ruelle distributions and residues of…
The hybrid Monte Carlo (HMC) algorithm is a ubiquitous method in computational physics with applications ranging from condensed matter to lattice QCD and beyond. However, HMC simulations often suffer from long autocorrelation times,…
We present an efficient numerical scheme based on Monte Carlo integration to approximate statistical solutions of the incompressible Euler equations. The scheme is based on finite volume methods, which provide a more flexible framework than…
A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…
We study the rate of convergence to equilibrium of the self-repellent random walk and its local time process on the discrete circle $\mathbb{Z}_n$. While the self-repellent random walk alone is non-Markovian since the jump rates depend on…