Related papers: A Monte Carlo method for computing the action of a…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…
The Markov chain Monte Carlo (MCMC) method is used to evaluate the imaginary-time path integral of a quantum oscillator with a potential that includes both a quadratic term and a quartic term whose coupling is varied by several orders of…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling…
In this work, we developed an efficient approach to compute ensemble averages in systems with pairwise-additive energetic interactions between the entities. Methods involving full enumeration of the configuration space result in exponential…
We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018)), where the manifold is defined by…
A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…
In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…
The Monte Carlo method is a thriving and mathematically beautiful numerical technique used extensively, nowadays, to deal with many demanding problems in diverse fields. Here, we present an iterative Monte Carlo algorithm to work out very…
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. In some cases, like in the…
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…
Iterative methods for computing matrix functions have been extensively studied and their convergence speed can be significantly improved with the right tuning of parameters and by mixing different iteration types. Handtuning the design…
In this paper, we aim to compute numerical approximation integral by using an adaptive Monte Carlo algorithm. We propose a stratified sampling algorithm based on an iterative method which splits the strata following some quantities called…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…