Displaying similar documents to “Equality cases in the symmetrization inequalities for Brownian transition functions and Dirichlet heat kernels.”

On nodal sets and nodal domains on S 2 and 2

Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili (2007)

Annales de l’institut Fourier

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We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on S 2 . We also construct a solution of the equation Δ u = u in 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

Multifractal properties of the sets of zeroes of Brownian paths

Dmitry Dolgopyat, Vadim Sidorov (1995)

Fundamenta Mathematicae

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We study Brownian zeroes in the neighborhood of which one can observe a non-typical growth rate of Brownian excursions. We interpret the multifractal curve for the Brownian zeroes calculated in [6] as the Hausdorff dimension of certain sets. This provides an example of the multifractal analysis of a statistically self-similar random fractal when both the spacing and the size of the corresponding nested sets are random.