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13 papers · 2 filters
Quantum Chaos for point scatterers on flat tori
Henrik Ueberschaer
This survey article deals with a delta potential - also known as a point scatterer - on flat 2D and 3D tori. We introduce the main conjectures regarding the spectral and wave funct…
The Coefficient Problem and Multifractality of Whole-Plane SLE and LLE
Bertrand Duplantier, Nguyen Thi Phuong Chi, Nguyen Thi Thuy Nga +1
We revisit the Bieberbach conjecture in the framework of SLE processes and, more generally, Lévy processes. The study of their unbounded whole-plane versions leads to a discrete se…
Think globally, compute locally
Vincent Bouchard, Bertrand Eynard
We introduce a new formulation of the so-called topological recursion, that is defined globally on a compact Riemann surface. We prove that it is equivalent to the generalized recu…
Universal shocks in the Wishart random matrix ensemble - 1
Jean-Paul Blaizot, Maciej A. Nowak, Piotr Warchoł
We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitr…
The Lyapunov exponent of products of random matrices close to the identity
A. Comtet, J. M. Luck, C. Texier +1
We study products of arbitrary random real matrices that are close to the identity matrix. Using the Iwasawa decomposition of , we identify a…
Rectangular amplitudes, conformal blocks, and applications to loop models
Roberto Bondesan, Jesper Lykke Jacobsen, Hubert Saleur
In this paper we continue the investigation of partition functions of critical systems on a rectangle initiated in [R. Bondesan et al, Nucl.Phys.B862:553-575,2012]. Here we develop…