On the rate of convergence in the central limit theorem for hierarchical Laplacians
ESAIM: Probability and Statistics, Tome 23 (2019), pp. 68-81

Let (X, d) be a proper ultrametric space. Given a measure m on X and a function B↦C(B) defined on the set of all non-singleton balls B we consider the hierarchical Laplacian L = L$$. Choosing a sequence {ε(B)} of i.i.d. random variables we define the perturbed function C(B, ω) and the perturbed hierarchical Laplacian L$$ = L$$. We study the arithmetic means $$ of the L$$-eigenvalues. Under certain assumptions the normalized arithmetic means $$ converge in law to the standard normal distribution. In this note we study convergence in the total variation distance and estimate the rate of convergence.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2018010
Classification : 12H25, 60F05, 94A17, 47S10, 60J25
Keywords: Ultrametric space, p-adic numbers, hierarchical Laplacian, fractional derivative, total variation and entropy distance

Bendikov, Alexander 1 ; Cygan, Wojciech 1

1 
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     title = {On the rate of convergence in the central limit theorem for hierarchical {Laplacians}},
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     pages = {68--81},
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Bendikov, Alexander; Cygan, Wojciech. On the rate of convergence in the central limit theorem for hierarchical Laplacians. ESAIM: Probability and Statistics, Tome 23 (2019), pp. 68-81. doi: 10.1051/ps/2018010

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