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Utility based methods provide a very general theoretically consistent approach to pricing and hedging of securities in incomplete financial markets. Solving problems in the utility based framework typically involves dynamic programming,…
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…
We present a Monte Carlo study of the two-component $\phi^4$ model on the simple cubic lattice in three dimensions. By suitable tuning of the coupling constant $\lambda$ we eliminate leading order corrections to scaling. High statistics…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three…
We introduce a Monte Carlo method, as a modification of existing cluster algorithms, which allows simulations directly on systems of infinite size, and for quantum models also at beta=infinity. All two-point functions can be obtained,…
Monte-Carlo (MC) methods, based on random updates and the trial-and-error principle, are well suited to retrieve particle size distributions from small-angle scattering patterns of dilute solutions of scatterers. The size sensitivity of…
We present a Monte Carlo method to compute efficiently susceptibilites or covariances of two physical variables. The method relies on a generalization of the exchange cluster algorithm to any model of interacting particles with any $2$-body…
We present a new approach to determine the small-scale statistical behavior of hydrodynamic turbulence by means of lattice simulations. Using the functional integral representation of the random-force-driven Burgers equation we show that…
We study the site-diluted Ising model in two dimensions with Monte Carlo simulations. Using finite-size scaling techniques we compute the critical exponents observing deviations from the pure Ising ones. The differences can be explained as…
Towards a solution to the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
We introduce a class of Monte Carlo estimators that aim to overcome the rapid growth of variance with dimension often observed for standard estimators by exploiting the target's independence structure. We identify the most basic…
Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…
Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
Many strongly correlated states, such as those arising in the fractional quantum Hall effect and spin liquids, are described by wave functions obtained by dividing particles into multiple clusters, constructing a readily evaluable wave…
In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…