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Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups

Pierre Del Moral, L. Miclo (2003)

ESAIM: Probability and Statistics

We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine...

Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups

Pierre Del Moral, L. Miclo (2010)

ESAIM: Probability and Statistics

We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V. These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We...

Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations ⋆⋆⋆

Romain Nguyen van yen, Éric Sonnendrücker, Kai Schneider, Marie Farge (2011)

ESAIM: Proceedings

A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by...

Particles, phases, fields

L. Wojtczak, A. Urbaniak-Kucharczyk, I. Zasada, J. Rutkowski (1996)

Banach Center Publications

The physical properties of particles and phasesare considered in connection with their description by means of the deformation of space-time. The analogy between particle trajectories and phase boundaries is discussed. The geometry and its curvature is related to the Clifford algebraic structure whose construction in terms of the theory of deformation leads to the expected solutions for correlation functions referring to spectroscopy and scattering problems. The stochastic nature of space-time is...

Past, Present and Future of Brain Stimulation

J. Modolo, R. Edwards, J. Campagnaud, B. Bhattacharya, A. Beuter (2010)

Mathematical Modelling of Natural Phenomena

Recent technological advances including brain imaging (higher resolution in space and time), miniaturization of integrated circuits (nanotechnologies), and acceleration of computation speed (Moore’s Law), combined with interpenetration between neuroscience, mathematics, and physics have led to the development of more biologically plausible computational models and novel therapeutic strategies. Today, mathematical models of irreversible medical conditions...

Perturbing the hexagonal circle packing: a percolation perspective

Itai Benjamini, Alexandre Stauffer (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hexagonal circle packing with radius 1 / 2 and perturb it by letting the circles move as independent Brownian motions for time t . It is shown that, for large enough t , if 𝛱 t is the point process given by the center of the circles at time t , then, as t , the critical radius for circles centered at 𝛱 t to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...

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