Ultrametric logarithm laws, II
نویسندگان
چکیده
منابع مشابه
Ultrametric Logarithm Laws I.
We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.
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Stronger versions of laws of the iterated logarithm for self-normalized sums of i.i.d. random variables are proved.
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In this paper we generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a sequence of subsets {At | t ∈ N} of a homogeneous space G/Γ (G a semisimple Lie group, Γ an irreducible lattice) and a sequence of elements ft of G under which #{t ∈ N | ftx ∈ At} is infinite for a.e. x ∈ G/Γ. The main tool is exponential decay of correlation coefficients of smooth fu...
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We generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a measure preserving system (X,μ, g) and a family of subsets {An | n ∈ N} of X under which #{1 ≤ n ≤ N | gnx ∈ An} is for μa.e. x ∈ X asymptotically (as N →∞) equal to PN n=1 μ(An). These conditions can be verified for various special cases of systems (X,μ, g, {An}), including actions of nonquasiunip...
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Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β > 0.
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2012
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-012-0376-y