Wenn Gemeindeteams "Leitung" übernehmen. Die transformative Kraft von Gemeindeteams in den Netzwerkstrukturen im pastoralen Raum - Modellraum 4 - Reis, Oliver; Hofmeister, Lisa; Burke, Rebekka

How children co-construct a religious abstract concept with their caregivers: Theological models in dialogue with linguistic semantics - Reis, Oliver; Viertel, Franziska (religions)

Was ist das "Katholische" einer Schule? Drei Zugänge auf zukünftige Herausforderungen - Reis, Oliver; Hoyer, Isabelle (Kirche und Schule. Die Fachzeitschrift der Hauptabteilung Schule und Erziehung)

Religion Lernen. Jahrbuch für konstruktivistische Religionspädagogik

Wie sich als Verband zum Religionsunterricht positionieren - Reis, Oliver; Mellentin, Franziska; Theis, Joachim; Tomberg, Markus; Wedding, Michael (Katechetische Blätter)

Modellprojekt Entwicklung der ehrenamtlichen Mitverantwortung. Projektbericht 2: Wenn Gemeindeteams "Leitung" übernehmen - Reis, Oliver; Kolk, Matthias

Die Kunst des Störens - eine komplexe Rekonstruktion pragmatischer Rahmungen - Reis, Oliver; Maurer, Kristina (Religion lernen. Jahrbuch für konstruktivistische Religionsdidaktik)

Mut und Offenheit. Auf dem Weg in die Zukunft von Lehre und Hochschule - Reis, Oliver; Kros, Inga (Das Hochschulwesen. Forum für Hochschulforschung, - praxis und -politik)

Vom Lehramtsstudium her denken. Erfahrungen und Perspektiven für die Gestaltung theologischer Studiengänge - Reis, Oliver (Lebendige Seelsorge)

When does the chaos in the Curie-Weiss model stop to propagate? - Jalowy, Jonas; Kabluchko, Zakhar; Löwe, Matthias; Marynych, Alexander (Electronic Journal of Probability)

Roots of polynomials under repeated differentiation and repeated applications of fractional differential operators - Hall, Brian C.; Ho, Ching-Wei; Jalowy, Jonas; Kabluchko, Zakhar (arXiv:2312.14883)
We start with a random polynomial $P^{N}$ of degree $N$ with independent coefficients and consider a new polynomial $P_{t}^{N}$ obtained by repeated applications of a fraction differential operator of the form $z^{a}% (d/dz)^{b},$ where $a$ and $b$ are real numbers. When $b>0,$ we compute the limiting root distribution $μ_{t}$ of $P_{t}^{N}$ as $N→∞.$ We show that $μ_{t}$ is the push-forward of the limiting root distribution of $P^{N}$ under a transport map $T_{t}$. The map $T_{t}$ is defined by flowing along the characteristic curves of the PDE satisfied by the log potential of $μ_{t}.$ In the special case of repeated differentiation, our results may be interpreted as saying that the roots evolve radially with constant speed until they hit the origin, at which point, they cease to exist. For general $a$ and $b,$ the transport map $T_{t}$ has a free probability interpretation as multiplication of an $R$-diagonal operator by an $R$-diagonal "transport operator." As an application, we obtain a push-forward characterization of the free self-convolution semigroup $\oplus$ of radial measures on $\mathbb{C}$. We also consider the case $b<0,$ which includes the case of repeated integration. More complicated behavior of the roots can occur in this case.

Zeros of random polynomials undergoing the heat flow - Hall, Brian C.; Ho, Ching-Wei; Jalowy, Jonas; Kabluchko, Zakhar (arXiv:2308.11685)
We investigate the evolution of the empirical distribution of the complex roots of high-degree random polynomials, when the polynomial undergoes the heat flow. In one prominent example of Weyl polynomials, the limiting zero distribution evolves from the circular law into the elliptic law until it collapses to the Wigner semicircle law, as was recently conjectured for characteristic polynomials of random matrices by Hall and Ho, 2022. Moreover, for a general family of random polynomials with independent coefficients and isotropic limiting distribution of zeros, we determine the zero distribution of the heat-evolved polynomials in terms of its logarithmic potential. Furthermore, we explicitly identify two critical time thresholds, at which singularities develop and at which the limiting distribution collapses to the semicircle law. We completely characterize the limiting root distribution of the heat-evolved polynomials before singularities develop as the push-forward of the initial distribution under a transport map. Finally, we discuss the results from the perspectives of partial differential equations (in particular Hamilton-Jacobi equation and Burgers' equation), optimal transport, and free probability. The theory is accompanied by explicit examples, simulations, and conjectures.

Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy - Erbar, Matthias; Huesmann, Martin; Jalowy, Jonas; Müller, Bastian (arXiv:2304.11145)
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation between two stationary random measures along a shortest curve connecting them. In the setting of stationary point processes we leverage this transport distance to give a geometric interpretation for the evolution of infinite particle systems with stationary distribution. Namely, we characterise the evolution of infinitely many Brownian motions as the gradient flow of the specific relative entropy w.r.t.~the Poisson point process. Further, we establish displacement convexity of the specific relative entropy along optimal interpolations of point processes and establish an stationary analogue of the HWI inequality, relating specific entropy, transport distance, and a specific relative Fisher information.

Optimal transport of stationary point processes: Metric structure, gradient flow and convexity of the specific entropy - Erbar, Matthias; Huesmann, Martin; Jalowy, Jonas; Müller, Bastian (arXiv:2304.11145)
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation between two stationary random measures along a shortest curve connecting them. In the setting of stationary point processes we leverage this transport distance to give a geometric interpretation for the evolution of infinite particle systems with stationary distribution. Namely, we characterise the evolution of infinitely many Brownian motions as the gradient flow of the specific relative entropy w.r.t.~the Poisson point process. Further, we establish displacement convexity of the specific relative entropy along optimal interpolations of point processes and establish an stationary analogue of the HWI inequality, relating specific entropy, transport distance, and a specific relative Fisher information.

The Wasserstein distance to the circular law - Jalowy, Jonas (Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)

The heat flow, GAF, and SL(2;R) - Hall, Brian; Ho, Ching-Wei; Jalowy, Jonas; Kabluchko, Zakhar (arXiv:2304.06665)
We establish basic properties of the heat flow on entire holomorphic functions that have order at most 2. We then look specifically at the action of the heat flow on the Gaussian analytic function (GAF). We show that applying the heat flow to a GAF and then rescaling and multiplying by an exponential of a quadratic function gives another GAF. It follows that the zeros of the GAF are invariant in distribution under the heat flow, up to a simple rescaling. We then show that the zeros of the GAF evolve under the heat flow approximately along straight lines, with an error whose distribution is independent of the starting point. Finally, we connect the heat flow on the GAF to the metaplectic representation of the double cover of the group $SL(2;\mathbb{R}).$

Gebaute Heiligung. Wie Stadtumbau und Heiligenverehrung des späten 17. und frühen 18. Jahrhunderts Paderborn in eine heilige Stadt verwandelten - Süßmann, Johannes ((Un)verfügbar – Kulturen des Heiligen)
Nach dem Dreißigjährigen Krieg kam es in Paderborn zu einem Stadtumbau. Unter der Regierung des Fürstbischofs Ferdinand von Fürstenberg (1661–1683) wurden drei neue Kirchen errichtet, eine ältere erhielt eine neue Fassade. Das machte alle vier zu städtebaulichen Dominanten – nicht nur durch Größe und Positionierung, sondern weil sie die Barockfassade in Paderborn einführten und damit die Kirchen in ein neues Verhältnis zum städtischen Raum rückten. Gestaltet als Schaufronten vor bühnenartigen Vorplätzen, trugen die Fassaden dazu bei, die vorher auf die Innenräume beschränkte Heiligenverehrung in den Stadtraum hinaus zu wenden und auch im Alltag vor Augen zu stellen. Zugleich wurde ein neuer Prozessionsweg geschaffen, der die Verehrung aller Kirchenpatrone zusammenführte und zu einer Aufgabe für die gesamte Stadt machte. Über Wallfahrtskapellen bezog man das Umland mit ein. Das gesamte Fürstbistum wurde geheiligt. Der politische Sinn war, es nach den Erschütterungen des Dreißigjährigen Kriegs im Innern neu zu begründen und nach außen sakrosankt zu machen.

Gegenreformation und verpasste Aufklärung. Die Academia Theodoriana im 17. und 18. Jahrhundert und ihr Verhältnis zu den heutigen Paderborner Hochschulen - Süßmann, Johannes (Westfälische Zeitschrift)
Keywords: Universität Paderborn; Jesuiten; Universitätsgeschichte; Bildungstheorie

Bibliotheken des Hellwegraums als Orte frühneuzeitlichen Kulturtransfers. Aufriß und Forschungsprogramm - Süßmann, Johannes (Bücher in Westfalen – Westfalen und ihre Bücher. Festschrift für Hermann-Josef Schmalor zum 70. Geburtstag)

Pantheon - Süßmann, Johannes