5 papers · 1 filter
Normal and Poisson approximation for Gibbs point processes with pair potentials
Christian Hirsch, Moritz Otto, Anne Marie Svane
We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals…
The asymptotic distribution of the scaled remainder for pseudo golden ratio expansions of a continuous random variable
Ira W. Herbst, Jesper Møller, Anne Marie Svane
Let be the base- expansion of a continuous random variable on the unit interval where is the positive solution to $β^n = 1 + β+ \cdots +…
The asymptotic distribution of the remainder in a certain base- expansion
Ira W. Herbst, Jesper Møller, Anne Marie Svane
Let be the base- expansion of a continuous random variable on the unit interval where is the golden ratio. We study the asymptotic distr…
Normal approximation for Gibbs processes via disagreement couplings
Christian Hirsch, Moritz Otto, Anne Marie Svane
This work improves the existing central limit theorems (CLTs) for geometric functionals of Gibbs processes in three aspects. First, we derive a CLT for weakly stabilizing functiona…
How many digits are needed?
Ira W. Herbst, Jesper Møller, Anne Marie Svane
Let be the digits in the base- expansion of a random variable defined on where is an integer. For , we study the probability distrib…