相关论文: Discrepancy between Monte-Carlo Results and Analyt…

We consider estimating an expected infinite-horizon cumulative discounted cost/reward contingent on an underlying stochastic process by Monte Carlo simulation. An unbiased estimator based on truncating the cumulative cost at a random…

We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $\sigma$-model at correlation lengths $\xi$ up to $\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte…

Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…

In this note, we assess the accuracy of CLT-based approximations for the volume of intersection of the $d$-dimensional cube $[-1,1]^d$ and an $L_q$-ball centred at the origin; this is clearly equivalent to approximating the distribution of…

The mean volume reflection angle of a high-energy charged particle passing through a bent crystal is expressed as an integral involving the effective interplanar potential over a single crystal period. Implications for positively and…

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) $\pi$ a given, general probability measure on $(\mathbb{R}^d,\mathcal{B}(\mathbb{R}^d))$ that is absolutely continuous with respect to a standard Gaussian…

In this paper, the binary random packing fraction of similar particles with size ratios ranging from unity to well over 2 is studied. The classic excluded volume model for spherocylinders and cylinders proposed by Onsager [1] is revisited…

We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…

Numerical simulations of models and theories that describe complex systems such as spin glasses are becoming increasingly important. Beyond fundamental research, these computational methods also find practical applications in fields like…

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any…

We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…

Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…

This paper concerns numerical assessment of Monte Carlo error in particle filters. We show that by keeping track of certain key features of the genealogical structure arising from resampling operations, it is possible to estimate variances…

We study coarsening phenomena in three different simple exclusion processes with quenched disordered jump rates. In the case of the totally asymmetric process, an earlier phenomenological description is improved, yielding for the time…

Let $X_1,\ldots,X_n$ be a standard normal sample in $\mathbb R^d$. We compute exactly the expected volume of the Gaussian polytope $\mathrm{conv}[X_1,\ldots,X_n]$, the symmetric Gaussian polytope $\mathrm{conv}[\pm X_1,\ldots,\pm X_n]$, and…

Counting experiments often rely on Monte Carlo simulations for predictions of Poisson expectations. The accompanying uncertainty from the finite Monte Carlo sample size can be incorporated into parameter estimation by modifying the Poisson…

Beam dump experiments have been used to search for new particles with null results interpreted in terms of limits on masses $m_\phi$ and coupling constants $\epsilon$. However these limits have been obtained by using approximations…

This paper investigates the impact of Malmquist bias on the distance to the Virgo cluster determined by the H_0 Key Project using M100, and consequently on the derived value of H_0. Malmquist bias is a volume-induced statistical effect…

It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In…

The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the…