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Diffusion Monte Carlo method: Numerical Analysis in a Simple Case

Mohamed El Makrini, Benjamin Jourdain, Tony Lelièvre (2007)

ESAIM: Mathematical Modelling and Numerical Analysis


The Diffusion Monte Carlo method is devoted to the computation of electronic ground-state energies of molecules. In this paper, we focus on implementations of this method which consist in exploring the configuration space with a fixed number of random walkers evolving according to a stochastic differential equation discretized in time. We allow stochastic reconfigurations of the walkers to reduce the discrepancy between the weights that they carry. On a simple one-dimensional example, we prove...

Disconnections of plane continua

Bajguz, W. (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

The paper deals with locally connected continua X in the Euclidean plane. Theorem 1 asserts that there exists a simple closed curve in X that separates two given points x , y of X if there is a subset L of X (a point or an arc) with this property. In Theorem 2 the two points x , y are replaced by two closed and connected disjoint subsets A , B . Again – under some additional preconditions – the existence of a simple closed curve disconnecting A and B is stated.

Distribution laws for integrable eigenfunctions

Bernard Shiffman, Tatsuya Tate, Steve Zelditch (2004)

Annales de l’institut Fourier

We determine the asymptotics of the joint eigenfunctions of the torus action on a toric Kähler variety. Such varieties are models of completely integrable systems in complex geometry. We first determine the pointwise asymptotics of the eigenfunctions, which show that they behave like Gaussians centered at the corresponding classical torus. We then show that there is a universal Gaussian scaling limit of the distribution function near its center. We also determine the limit...

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