arXiv subjects

Zhiqiang Gao

Publications and source records attributed to Zhiqiang Gao.

38 records · Page 3Linked to original sources

arXiv2013

Stable laws and spectral gap properties for affine random walks

We consider a general multidimensional affine recursion with corresponding Markov operator $P$ and a unique $P$-stationary measure. We show spectral gap properties on Hölder spaces for the corresponding Fourier operators and we deduce convergence to stable laws for the Birkhoff sums along the recursion. The parameters of the stable laws are expressed in terms of basic quantities depending essentially on the matricial multiplicative part of $P$. Spectral gap properties of $P$ and homogeneity at infinity of the $P$-stationary measure play an important role in the proofs.

math.PR↗

arXiv2012

Criterions of Wiener type for minimally thin sets and rarefied sets associated with the stationary Schrödinger operator in a cone

In the paper we give some criterions for a-minimally thin sets and a-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or {\infty} with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside a-rarefied set. Finally we illustrate the relation between a-minimally thin set and a-rarefied set in a cone.

math.CA↗