Related papers: Superbosonisation via Riesz superdistributions
This is the extended version of a survey prepared for publication in the Springer INdAM series. Superbosonisation, introduced by Littelmann-Sommers-Zirnbauer, is a generalisation of bosonisation, with applications in Random Matrix Theory…
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
Superbosonization is a new variant of the method of commuting and anti-commuting variables as used in studying random matrix models of disordered and chaotic quantum systems. We here give a concise mathematical exposition of the key…
Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard-Stratonovich…
Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The…
Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random…
The Wishart probability distribution on symmetricmatrices has been initially defined by mean of the multivariateGaussian distribution as an of the chi-square distribution. A moregeneral definition is given using results for harmonic…
Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary…
Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the…
We develop a theory of multidimensional randomization in Lebesgue spaces $L^p$ with the aid of Kahane-Khintchine-Marcus-Pisier inequalities. More precisely, we obtain a result in the spirit of Maurey-Pisier's theorem which involves random…
The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of…
In the last few years, the supersymmetry method was generalized to real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic group, respectively.…
Supersymmetry is nowadays indispensable for many problems in Random Matrix Theory. It is presented here with an emphasis on conceptual and structural issues. An introduction to supermathematics is given. The Hubbard-Stratonovich…
This article derives the distribution of random matrix $\mathbf{X}$ associated with the transformation $\mathbf{Y} = \mathbf{X}^{*}\mathbf{X}$, such that $\mathbf{Y}$ has a Riesz distribution for real normed division algebras. Two versions…
We study the propagation of time-harmonic acoustic or transverse magnetic (TM) polarized electromagnetic waves in a periodic waveguide lying in the semi-strip $(0,\infty)\times(0,L)$. It is shown that there exists a Riesz basis of the space…
We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelh{\"o}f Hypothesis and the Riemann…
The Epstein--Glaser type T-subtraction introduced by one of the authors in a previous paper is extended to the Lorentz invariant framework. The advantage of using our subtraction instead of Epstein and Glaser's standard W-subtraction method…
We study infinitely divisible (ID) distributions on the nonnegative half-line $\mathbb{R}_+$. The L\'{e}vy-Khintchine representation of such distributions is well-known. Our primary contribution is to cast the probabilistic objects and the…
This article is intended to provide a pedagogical introduction to the supersymmetry method for performing ensemble-averaging in Gaussian random-matrix theory. The method is illustrated by a detailed calculation of the simplest non-trivial…
The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function…