Michael Voit
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View article: An estimate for $β$-Hermite ensembles via the zeros of Hermite polynomials
An estimate for $β$-Hermite ensembles via the zeros of Hermite polynomials Open
Let $X$ be an $N$-dimensional random vector which describes the ordered eigenvalues of a $β$-Hermite ensemble, and let $z$ the vector containing the ordered zeros of the Hermite poynomial $H_N$. We present an explicit estimate for $P(\|X-z…
View article: On the extremal eigenvalues of Jacobi ensembles at zero temperature
On the extremal eigenvalues of Jacobi ensembles at zero temperature Open
For the $β$-Hermite, Laguerre, and Jacobi ensembles of dimension $N$ there exist central limit theorems for the freezing case $β\to\infty$ such that the associated means and covariances can be expressed in terms of the associated Hermite, …
View article: An explicit formula for free multiplicative Brownian motions via spherical functions
An explicit formula for free multiplicative Brownian motions via spherical functions Open
After some normalization, the logarithms of the ordered singular values of Brownian motions on $GL(N,\mathbb F)$ with $\mathbb F=\mathbb R, \mathbb C$ form Weyl-group invariant Heckman-Opdam processes on $\mathbb R^N$ of type $A_{N-1}$. We…
View article: On the differential equations of frozen Calogero-Moser-Sutherland particle models
On the differential equations of frozen Calogero-Moser-Sutherland particle models Open
Multivariate Bessel and Jacobi processes describe Calogero-Moser-Sutherland particle models.They depend on a parameter k and are related to time-dependent classical random matrix models like Dysom Brownian motions, where k has the interpre…
View article: On the differential equations of frozen Calogero-Moser-Sutherland particle models
On the differential equations of frozen Calogero-Moser-Sutherland particle models Open
Multivariate Bessel and Jacobi processes describe Calogero-Moser-Sutherland particle models. They depend on a parameter $k$ and are related to time-dependent classical random matrix models like Dysom Brownian motions, where $k$ has the int…
View article: DiffAnt: Diffusion Models for Action Anticipation
DiffAnt: Diffusion Models for Action Anticipation Open
Anticipating future actions is inherently uncertain. Given an observed video segment containing ongoing actions, multiple subsequent actions can plausibly follow. This uncertainty becomes even larger when predicting far into the future. Ho…
View article: A Survey on Deep Learning Techniques for Action Anticipation
A Survey on Deep Learning Techniques for Action Anticipation Open
The ability to anticipate possible future human actions is essential for a wide range of applications, including autonomous driving and human-robot interaction. Consequently, numerous methods have been introduced for action anticipation in…
View article: Freezing limits for Calogero–Moser–Sutherland particle models
Freezing limits for Calogero–Moser–Sutherland particle models Open
One‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of like Weyl chambers and alcoves with second‐order differential operators as generat…
View article: Anticipative Feature Fusion Transformer for Multi-Modal Action Anticipation
Anticipative Feature Fusion Transformer for Multi-Modal Action Anticipation Open
Although human action anticipation is a task which is inherently multi-modal, state-of-the-art methods on well known action anticipation datasets leverage this data by applying ensemble methods and averaging scores of unimodal anticipation…
View article: Freezing Limits for Beta-Cauchy Ensembles
Freezing Limits for Beta-Cauchy Ensembles Open
Bessel processes associated with the root systems $A_{N-1}$ and $B_N$ describe interacting particle systems with $N$ particles on $\mathbb R$; they form dynamic versions of the classical $\beta$-Hermite and Laguerre ensembles. In this pape…
View article: Freezing Limits for Beta-Cauchy Ensembles
Freezing Limits for Beta-Cauchy Ensembles Open
Bessel processes associated with the root systems $A_{N-1}$ and $B_N$ describe interacting particle systems with $N$ particles on $\mathbb R$; they form dynamic versions of the classical $β$-Hermite and Laguerre ensembles. In this paper we…
View article: Wigner- and Marchenko-Pastur-type limits for Jacobi processes
Wigner- and Marchenko-Pastur-type limits for Jacobi processes Open
We study Jacobi processes $(X_{t})_{t\ge0}$ on the compact spaces $[-1,1]^N$ and on the noncompact spaces $[1,\infty[^N$ which are motivated by the Heckman-Opdam theory for the root systems of type BC and associated integrable particle sys…
View article: Positivity of Gibbs states on distance-regular graphs
Positivity of Gibbs states on distance-regular graphs Open
We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes that the graph can be embedded into a growing family of distance-regular gra…
View article: Limit theorems for Jacobi ensembles with large parameters
Limit theorems for Jacobi ensembles with large parameters Open
Consider Jacobi random matrix ensembles with the distributions $$c_{k_1,k_2,k_3}\prod_{1\leq i< j \leq N}\left(x_j-x_i\right)^{k_3}\prod_{i=1}^N \left(1-x_i\right)^{\frac{k_1+k_2}{2}-\frac{1}{2}}\left(1+x_i\right)^{\frac{k_2}{2}-\frac{1}{2…
View article: Distances of roots of classical orthogonal polynomials
Distances of roots of classical orthogonal polynomials Open
Let $(P_N)_{N\ge0}$ one of the classical sequences of orthogonal polynomials, i.e., Hermite, Laguerre or Jacobi polynomials. For the roots $z_{1,N},\ldots, z_{N,N}$ of $P_N$ we derive lower estimates for $\min_{i\ne j}|z_{i,N}-z_{j,N}|$ an…
View article: An Evaluation of Different Methods for 3D-Driver-Body-Pose Estimation
An Evaluation of Different Methods for 3D-Driver-Body-Pose Estimation Open
Driver monitoring systems are increasingly introduced in modern commercial vehicles. Their importance will rise with automated vehicles, requiring the driver to pay attention or to take over in a timely manner. With the success of deep lea…
View article: Secure and Privacy-Respecting Documentation for Interactive Manufacturing and Quality Assurance
Secure and Privacy-Respecting Documentation for Interactive Manufacturing and Quality Assurance Open
The automated documentation of work steps is a requirement of many modern manufacturing processes. Especially when it comes to important procedures such as safety critical screw connections or weld seams, the correct and complete execution…
View article: Elementary symmetric polynomials and martingales for Heckman-Opdam processes
Elementary symmetric polynomials and martingales for Heckman-Opdam processes Open
We consider the generators $L_k$ of Heckman-Opdam diffusion processes in the compact and non-compact case in $N$ dimensions for root systems of type $A$ and $B$, with a multiplicity function of the form $k=κk_0$ with some fixed value $k_0$…
View article: Bias in Knowledge Graphs - An Empirical Study with Movie Recommendation and Different Language Editions of DBpedia
Bias in Knowledge Graphs - An Empirical Study with Movie Recommendation and Different Language Editions of DBpedia Open
Public knowledge graphs such as DBpedia and Wikidata have been recognized as interesting sources of background knowledge to build content-based recommender systems. They can be used to add information about the items to be recommended and …
View article: Bias in Knowledge Graphs - An Empirical Study with Movie Recommendation and Different Language Editions of DBpedia
Bias in Knowledge Graphs - An Empirical Study with Movie Recommendation and Different Language Editions of DBpedia Open
Public knowledge graphs such as DBpedia and Wikidata have been recognized as interesting sources of background knowledge to build content-based recommender systems. They can be used to add information about the items to be recommended and …
View article: Dynamic Interaction Graphs for Driver Activity Recognition
Dynamic Interaction Graphs for Driver Activity Recognition Open
The drivers activities and the resulting distraction is relevant for all levels of vehicle automation. It is especially important for take-over scenarios in partially automated vehicles. To this end we investigate graph neuronal networks f…
View article: The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime
The differential equations associated with Calogero-Moser-Sutherland particle models in the freezing regime Open
Multivariate Bessel processes describe Calogero-Moser-Sutherland particle models and are related with $β$-Hermite and $β$-Laguerre ensembles. They depend on a root system and a multiplicity $k$. Recently, several limit theorems for $k\to\i…
View article: Functional central limit theorems for multivariate Bessel processes in the freezing regime
Functional central limit theorems for multivariate Bessel processes in the freezing regime Open
Multivariate Bessel processes $(X_{t,k})_{t\ge0}$ describe interacting particle systems of Calogero-Moser-Sutherland type and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles. They depend on a root system and a multiplicity …