Related papers: Statistical estimation of percolation cluster para…
We review the method of stochastic error correction which eliminates the truncation error associated with any subspace diagonalization. Monte Carlo sampling is used to compute the contribution of the remaining basis vectors not included in…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
We consider the percolation problem of sites on an $L\times L$ square lattice with periodic boundary conditions which were unvisited by a random walk of $N=uL^2$ steps, i.e. are vacant. Most of the results are obtained from numerical…
We study the porosity properties of fractal percolation sets $E\subset\mathbb{R}^d$. Among other things, for all $0<\varepsilon<\tfrac12$, we obtain dimension bounds for the set of exceptional points where the upper porosity of $E$ is less…
Using methods of conformal field theory, we conjecture an exact form for the probability that n distinct clusters span a large rectangle or open cylinder of aspect ratio k, in the limit when k is large.
By considering the effect of varying the target radii and detector aperture width on the scattering angle in experimental Compton scattering, mathematical models were developed and subsequently incorporated into Monte Carlo simulations. By…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
We introduce several infinite families of new critical exponents for the random-cluster model and present scaling arguments relating them to the k-arm exponents. We then present Monte Carlo simulations confirming these predictions. These…
Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses…
Monte Carlo methods are widely used to estimate observables in many-body quantum systems. However, conventional sampling schemes often require a large number of samples to achieve sufficient accuracy. In this work we propose the…
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is…
Distortion risk measures play a critical role in quantifying risks associated with uncertain outcomes. Accurately estimating these risk measures in the context of computationally expensive simulation models that lack analytical tractability…
A Monte Carlo based computer model is presented to comprehend the contrasting observations of Mazumder et al. [Phys. Rev. Lett. 93, 255704 (2004) and Phys. Rev. B 72, 224208 (2005)], based on neutron-scattering measurements, on temporal…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
The review is a brief description of the state of problems in percolation theory and their numerous applications, which are analyzed on base of interesting papers published in the last 15-20 years. At the submitted papers are studied both…
Quantitative photoacoustic tomography aims at estimating optical parameters from photoacoustic images that are formed utilizing the photoacoustic effect caused by the absorption of an externally introduced light pulse. This optical…
A probabilistic approach for estimating sample qualities for stochastic differential equations is introduced in this paper. The aim is to provide a quantitative upper bound of the distance between the invariant probability measure of a…
Extant "fast" algorithms for Monte Carlo confidence sets are limited to univariate shift parameters for the one-sample and two-sample problems using the sample mean as the test statistic; moreover, some do not converge reliably and most do…