Convergence in Total Variation for nonlinear functionals of random hyperspherical harmonics

Random hyperspherical harmonics are Gaussian Laplace eigenfunctions on the unit d-dimensional sphere (d >= 2). We study the convergence in Total Variation distance for their nonlinear statistics in the high energy limit, i.e., for diverging sequences of Laplace eigenvalues. Our approach takes advantage of a recent result by Bally, Caramellino and Poly (2020): combining the Central Limit Theorem in Wasserstein distance obtained by Marinucci and Rossi (2015) for Hermite-rank 2 functionals with new results on the asymptotic behavior of their Malliavin-Sobolev norms, we are able to establish second order Gaussian fluctuations in this stronger probability metric as soon as the functional is regular enough. Our argument requires some novel estimates on moments of products of Gegenbauer polynomials that may be of independent interest, which we prove via the link between graph theory and diagram formulas. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:/

"Mapping the Discourse. Architecture Periodicals in/for the Teaching of Architecture History/ Une cartographie du discours. Périodiques d’architecture dans/pour l’enseignement de l’histoire de l’architecture".

The article reflects on a pedagogical project conducted in the framework of the History and Theory course at Politecnico di Milano and questions the value of architectural journals as sources, instruments, methods, and narrative devices for the teaching of architectural history, probing their role as mediators with multifaceted networks of professional, intellectual, and institutional milieux involved in the production of architectural knowledge. The study was conducted on a corpus of around fifty periodicals addressed as a “system of knowledge”, crossing diverse genres and generations of journals, and questioning their character of “complex social objects” to be investigated in their material, economic, cultural, and visual dimensions. On the one hand, the method combining “journal biographies” with the decoding of the issues through the analysis of all their structuring parts allows questioning the changing notion of milieu that magazines contribute to creating over time, revealing the interrelations between a constellation of agents - editors, owners, institutions, and audience – with their divergent agendas, rationalities, and editorial strategies. On the other hand, the paper reflects on the significance of analyzing journals in their interconnections, as cross-cultural and comparative readings offer a more nuanced understanding of the times and forms of production of architectural culture as a transnational practice, challenging the canonical interpretations and time frames of a 20th-century architectural history still centered on the European and North American editorial scene