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