arXiv subjects

Anselm Reichenbachs

Publications and source records attributed to Anselm Reichenbachs.

4 recordsLinked to original sources

arXiv2015

Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation

A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete Ornstein-Uhlenbeck semigroup. The result is applied to sub-graph counts and to the number of vertices having a prescribed degree in the Erdős-Renyi random graph. A further application deals with a percolation problem on trees.

math.PR↗

arXiv2014

Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences

Berry-Esseen bounds for non-linear functionals of infinite Rademacher sequences are derived by means of the Malliavin-Stein method. Moreover, multivariate extensions for vectors of Rademacher functionals are shown. The results establish a connection to small-ball probabilities and shed new light onto the relation between central limit theorems on the Rademacher chaos and norms of contraction operators. Applications concern infinite weighted 2-runs, a combinatorial central limit theorem and traces of Bernoulli random matrices.

math.PR↗

arXiv2012

On the accuracy of the normal approximation for the free energy in the REM

In the present paper we consider the fluctuations of the free energy in the random energy model (REM) on a moderate deviation scale. We find that for high temperatures the normal approximation holds only in a narrow range of scalings away from the CLT. For scalings of higher order, probabilities of moderate deviations decay faster than exponentially.

math.PR↗

arXiv2011

Moderate Deviations for a Curie-Weiss model with dynamical external field

In the present paper we prove moderate deviations for a Curie-Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard. The results extend those already obtained in the case of a constant external field by Eichelsbacher and Löwe. The Curie-Weiss model with dynamic external field is related to the so called dynamic Z-random walks. We also prove a moderate deviation result for the dynamic Z-random walk, completing the list of limit theorems for this object.

math.PR↗