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A central limit theorem on the space of positive definite symmetric matrices

Piotr Graczyk (1992)

Annales de l'institut Fourier

A central limit theorem is proved on the space 𝒫 n of positive definite symmetric matrices. To do this, some natural analogs of the mean and dispersion on 𝒫 n are defined and investigated. One uses a Taylor expansion of the spherical functions on 𝒫 n .

A Gaussian bound for convolutions of functions on locally compact groups

Nick Dungey (2006)

Studia Mathematica

We give new and general sufficient conditions for a Gaussian upper bound on the convolutions K m + n K m + n - 1 K m + 1 of a suitable sequence K₁, K₂, K₃, ... of complex-valued functions on a unimodular, compactly generated locally compact group. As applications, we obtain Gaussian bounds for convolutions of suitable probability densities, and for convolutions of small perturbations of densities.

A Littlewood-Paley-Stein estimate on graphs and groups

Nick Dungey (2008)

Studia Mathematica

We establish the boundedness in L q spaces, 1 < q ≤ 2, of a “vertical” Littlewood-Paley-Stein operator associated with a reversible random walk on a graph. This result extends to certain non-reversible random walks, including centered random walks on any finitely generated discrete group.

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