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Some stationary fields and their spectral measure on hyperbolic plane

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Brownian field on hyperbolic plane is a Gaussian field with stationary increments, and a Kintchine’s theorem associates with the variance of the increments a spectral measure. In this talk a formula for this spectral measure will be introduced. I will also consider some sationary fields associated with spherical functions. I will make comparisons with the Euclidean case and recall basic notions of hyperbolic geometry, to make the talk as self-contained as possible.

This talk is part of the Probability series.

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