The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory.  Subjects discussed in this Work are those treated in the so-called StrasbourgZürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum YangMills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributionsin this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.

Nalini Anantharaman is currently the Chair of the mathematics department at the University of Strasbourg. Analysis and mathematical physics are the main focus of Nalini Anantharamans research. She has studied chaos in wave propagation (quantum chaos) and, more recently, harmonic analysis on large graphs. She was elected in 2019 a member of the French academy of sciences and has been awarded many prestigious international prizes among which the Salem and Poincare prizes.

Ashkan Nikeghbali currently holds a Chair of applied mathematics at the institute of mathematics and at the department for banking and finance at the University of Zurich. His fields of interest include probability theory, random matrix theory, analytic number theory and quantitative finance. He also serves on several companies' advisory boards.

Michael Th. Rassias is a Research Fellow at the University of Zürich and a visiting researcher at the Institute for Advanced Study, Princeton. He has received several awards in mathematical problem-solving Olympiads as well as the Notara Prize by the Academy of Athens. His research interests lie in mathematical analysis, analytic number theory and their applications.

Monochromatic Random Waves for general Riemannian manifolds (Canzani).- A Brief Review of the ETH- Approach to Quantum Mechanics  (Fröhlich).- Linear and non-linear harmonic boundaries of graphs; an approach with p-cohomology in degree one (Gournay).- Polyharmonic functions for finite graphs and Markov chains (Hirschler).- Interacting electrons in a random medium: a simple one-dimensional model (Klopp).- Entropies for negatively curved manifolds (Ledrappie)- Two-dimensional quantum Yang-Mills theory and the Makeenko-Migdal equations (Lévy).- Limit operators for circular ensembles (Maples).- Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimension d 3 (Sohinger).- Interfaces in spectral asymptotics and nodal sets (Zelditch).