Mario Kieburg

Winding number statistics for chiral random matrices: Averaging ratios of determinants with parametric dependence

Nico Hahn, Mario Kieburg, Omri Gat, Thomas Guhr

Journal article  |  2023  |  JOURNAL OF MATHEMATICAL PHYSICS

Topological invariance is a powerful concept in different branches of physics as they are particularly robust under perturbations...

Derivative principles for invariant ensembles

M Kieburg, J Zhang

Journal article  |  2023  |  Advances in Mathematics

In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential..

Volume-Law Entanglement Entropy of Typical Pure Quantum States

Eugenio Bianchi, Lucas Hackl, Mario Kieburg, Marcos Rigol, Lev Vidmar

Journal article  |  2022  |  PRX QUANTUM

The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has recently been conjectured to b..

Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk

G Akemann, V Gorski, M Kieburg

Journal article  |  2022  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the sp..

Hard edge statistics of products of Pólya ensembles and shifted GUE's

M Kieburg

Journal article  |  2022  |  Journal of Approximation Theory

Very recently, we have shown how the harmonic analysis approach can be modified to deal with products of general Hermitian and com..

Local tail statistics of heavy-tailed random matrix ensembles with unitary invariance

M Kieburg, A Monteleone

Journal article  |  2021  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

We study heavy-tailed Hermitian random matrices that are unitarily invariant. The invariance implies that the eigenvalue and eigen..

Harmonic analysis for rank-1 randomised Horn problems

Jiyuan Zhang, Mario Kieburg, Peter J Forrester

Journal article  |  2021  |  LETTERS IN MATHEMATICAL PHYSICS

The randomised Horn problem, in both its additive and multiplicative versions, has recently drawn an increasing interest. Especial..

Page curve for fermionic Gaussian states

Eugenio Bianchi, Lucas Hackl, Mario Kieburg

Journal article  |  2021  |  PHYSICAL REVIEW B

In a seminal paper, Page found the exact formula for the average entanglement entropy for a pure random state. We consider the ana..

Cascade of phase transitions in a planar Dirac material

Takuya Kanazawa, Mario Kieburg, Jacobus JM Verbaarschot

Journal article  |  2021  |  JOURNAL OF HIGH ENERGY PHYSICS

We investigate a model of interacting Dirac fermions in 2 + 1 dimensions with M flavors and N colors having the U(M)×SU(N) symmetr..

New term in effective field theory at fixed topology

M Kieburg, M Lauritzen, BT Sogaard, K Splittorff

Journal article  |  2021  |  PHYSICAL REVIEW D

A random matrix model for lattice QCD which takes into account the positive definite nature of the Wilson term is introduced. The ..