138 research outputs found
Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
Contrary to the finite dimensional case, Weyl and Wick quantizations are no
more asymptotically equivalent in the infinite dimensional bosonic second
quantization. Moreover neither the Weyl calculus defined for cylindrical
symbols nor the Wick calculus defined for polynomials are preserved by the
action of a nonlinear flow. Nevertheless taking advantage carefully of the
information brought by these two calculuses in the mean field asymptotics, the
propagation of Wigner measures for general states can be proved, extending to
the infinite dimensional case a standard result of semiclassical analysis.Comment: 39 page
ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis
International audienceGiven a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the e ffect of each (group of) variable(s) and computing sensitivity indices without recursivity
Interplay of disorder and nonlinearity in Klein-Gordon models: Immobile kinks
We consider Klein-Gordon models with a -correlated spatial disorder.
We show that the properties of immobile kinks exhibit strong dependence on the
assumptions as to their statistical distribution over the minima of the
effective random potential. Namely, there exists a crossover from monotonically
increasing (when a kink occupies the deepest potential well) to the
non-monotonic (at equiprobable distribution of kinks over the potential minima)
dependence of the average kink width as a function of the disorder intensity.
We show also that the same crossover may take place with changing size of the
system.Comment: 7 pages, 4 figure
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