Publications associées à Felix Hausdorff

Hausdorff dimension of fermions on a random lattice

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 int ...

Elsevier2024

The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism

Cheuk Yin Lee

We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions. We also establish a Chung-type law of the iterated logarithm. The results ...

INT STATISTICAL INST2022

Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation

Maria Carola Colombo, Silja Noëmi Aline Haffter

We consider the SQG equation with dissipation given by a fractional Laplacian of order α

2021

Restriction of 3D arithmetic Laplace eigenfunctions to a plane

Riccardo Walter Maffucci

We consider a random Gaussian ensemble of Laplace eigenfunctions on the 3D torus, and investigate the 1-dimensional Hausdorff measure ('length') of nodal intersections against a smooth 2-dimensional toral sub-manifold ('surface'). A prior result of ours pr ...

2020

The First Passage Sets of the 2D Gaussian Free Field: Convergence and Isomorphisms

Juhan Aru, Titus Lupu

In a previous article, we introduced the first passage set (FPS) of constant level -aof the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the bo ...

SPRINGER2020

The complexity of error metrics

Mathias Soeken

Approximate computing exploits the fact that many applications do not require the results to be exact but not to exceed a threshold in a given error metric. Algorithms in approximate computing require to compute the error of the approximation in order to m ...

ELSEVIER SCIENCE BV2018

Moduli spaces of toric manifolds

Tudor Ratiu

We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-connectedness, compactness, and completeness. The construction of the distance i ...

Springer Verlag2014

Consistent Digital Line Segments

Doemoetoer Palvoelgyi

We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we show how to derive such a system of digital segments from any total order o ...

2012

Criteria for hitting probabilities with applications to systems of stochastic wave equations

Robert Dalang

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these ...

2010

Steiner's Invariants and Minimal Connections

Marc Troyanov, Stephen Ducret

The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure. ...

2008