Fractional dimension of sets in discrete spaces
暂无分享,去创建一个
The authors give a new definition dimH(A) for the dimension of an arbitrary subset of the lattice d. They establish elementary properties, and calculate the dimension for some examples. Finally, they announce a result which states that, if dimH(A) d-2 then A is recurrent.
[1] F. Spitzer. Principles Of Random Walk , 1966 .
[2] J. G. Wendel,et al. The exact hausdorff measure of the zero set of a stable process , 1966 .
[3] Curtis T. McMullen,et al. The Hausdorff dimension of general Sierpiński carpets , 1984, Nagoya Mathematical Journal.
[4] Michel L. Lapidus,et al. Tambour fractal: vers une résolution de la conjecture de Weyl-Berry pour les valeurs propres du laplacien , 1988 .
[5] John Lamperti,et al. Wiener's test and Markov chains , 1963 .