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Gaussian estimates for spatially inhomogeneous random walks on \(\mathbb Z^d\). (English) Zbl 1102.60062

Let \(\Gamma\) be a symmetric finite subset of \(\mathbb{Z}^d\), let \((S_j)_{j\in \mathbb{N}}\) be a spatially inhomogeneous random walk on \(\Gamma\) and let \(p_n(x,y)\) (\(n\in \mathbb{N}; x,y\in \mathbb{Z}^d\)) be the associated transition kernel. The author proves an upper and a lower estimation of \(p_n(x,y)\) in terms of the Gaussian density \(\exp(-{|x-y|^2}/{n})\).

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60J35 Transition functions, generators and resolvents
60J45 Probabilistic potential theory
31C20 Discrete potential theory
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