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Hidden Positivity and a New Approach to Numerical Computation of Hausdorff Dimension: Higher Order Methods [PDF]

, 2020
Richard S. Falk, Roger D. Nussbaum
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Hausdorff dimension of fermions on a random lattice

Nuclear Physics B
Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows the study of ...
Mattia Varrone, William E.V. Barker
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Generalized Dimensions of Self-Affine Sets with Overlaps

Fractal and Fractional
Two decades ago, Ngai and Wang introduced a well-known finite type condition (FTC) on the self-similar iterated function system (IFS) with overlaps and used it to calculate the Hausdorff dimension of self-similar sets. In this paper, inspired by Ngai and
Guanzhong Ma, Jun Luo, Xiao Zhou
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On spectra of probability measures generated by GLS-expansions

Modern Stochastics: Theory and Applications, 2016
We study properties of distributions of random variables with independent identically distributed symbols of generalized Lüroth series (GLS) expansions (the family of GLS-expansions contains Lüroth expansion and $Q_{\infty }$- and ${G_{\infty }^{2 ...
Marina Lupain
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Hausdorff dimension of collision times in one-dimensional log-gases

AIP Advances
We consider systems of multiple Brownian particles in one dimension that repel mutually via a logarithmic potential on the real line, more specifically the Dyson model.
Nicole Hufnagel, Sergio Andraus
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On the Hausdorff dimension of circular Furstenberg sets

Discrete Analysis
On the Hausdorff dimension of circular Furstenberg sets, Discrete Analysis 2024:18, 83 pp. In the late 1990s, Wolff proved the following result. Suppose that the set $E\subset \mathbb R^2$ contains circles centered at all points of a Borel set with ...
Katrin Fässler, Jiayin Liu, Tuomas Orponen   +2 more
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On the Computation of the Hausdorff Dimension of the Walrasian Economy:Further Notes [PDF]

: In a recent paper, Dominique (2009) argues that for a Walrasian economy with m consumers and n goods, the equilibrium set of prices becomes a fractal attractor due to continuous destructions and creations of excess demands.
Dominique, C-Rene
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Calculation of Hausdorff dimensions of basins of ergodic measures in encoding spaces

Журнал Белорусского государственного университета: Математика, информатика, 2018
In the article we consider spaces XN of sequences of elements of finite alphabet X (encoding spaces) and ergodic measures on them, basins of ergodic measures and Hausdorff dimensions of such basins with respect to ultrametrics defined by a product of ...
Pavel N. Varabei
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On the Visibility of Homogeneous Cantor Sets

Fractal and Fractional
The problems associated with the visible set have been explored by various scholars. In this paper, we investigate the Hausdorff dimension and the topological properties of the visible set in relation to the products of homogeneous Cantor sets.
Yi Cai, Yufei Chen
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Projections of measures with small supports

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2021
In this paper, we use a characterization of the mutual multifractal Hausdorff dimension in terms of auxiliary measures to investigate the projections of measures with small supports.
Bilel Selmi
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