Related papers: Monte Carlo Methods for the Self-Avoiding Walk

This paper proposes an eigenvalue-based small-sample approximation of the celebrated Markov Chain Monte Carlo that delivers an invariant steady-state distribution that is consistent with traditional Monte Carlo methods. The proposed…

Monte Carlo methods play an important role in scientific computation, especially when problems have a vast phase space. In this lecture an introduction to the Monte Carlo method is given. Concepts such as Markov chains, detailed balance,…

It is shown how to obtain accurate values for American options using Monte Carlo simulation. The main feature of the novel algorithm consists of tracking the boundary between exercise and hold regions via optimization of a certain payoff…

We develop statistical enumeration methods for self-avoiding walks using a powerful sampling technique called the multicanonical Monte Carlo method. Using these methods, we estimate the numbers of the two dimensional N-step self-avoiding…

In this article we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of 1-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS…

Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of…

We compute the exponent gamma for self-avoiding walks in three dimensions. We get gamma = 1.1575 +- 0.0006 in agreement with renormalization-group predictions. Earlier Monte Carlo and exact-enumeration determinations are now seen to be…

The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the self-avoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is…

World-line quantum Monte Carlo methods are reviewed with an emphasis on breakthroughs made in recent years. In particular, three algorithms -- the loop algorithm, the worm algorithm, and the directed-loop algorithm -- for updating…

We present a new Monte Carlo scheme for the efficient simulation of multi-polymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler,…

Random walks are frequently used as a model for very diverse physical phenomena. The Monte Carlo method is a versatile tool for the study of the properties of systems modelled as random walks. Often, each walker is associated with a…

In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimisation algorithms. In particular we prove the convergence of the proposed algorithms and derive the…

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…

Sequential Monte Carlo methods which involve sequential importance sampling and resampling are shown to provide a versatile approach to computing probabilities of rare events. By making use of martingale representations of the sequential…

Monte Carlo particle transport codes are well established on classical hardware and are considered as the reference tool for nuclear applications. In a growing number of domains, the design of algorithms is progressively shifting towards…

This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo…

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…

Based on the principles of importance sampling and resampling, sequential Monte Carlo (SMC) encompasses a large set of powerful techniques dealing with complex stochastic dynamic systems. Many of these systems possess strong memory, with…

A Monte Carlo method to optimize cuts on variables is presented and evaluated. The method gives a much higher signal to noise ratio than does a manual choice of cuts.

This paper presents a tool for addressing a key component in many algorithms for planning robot trajectories under uncertainty: evaluation of the safety of a robot whose actions are governed by a closed-loop feedback policy near a nominal…