Related papers: Complete diagrammatics of the single ring theorem
A map is given showing that convolutions of independent random variables over a finite group and matrix multiplications of doubly stochastic matrices are homomorphic. As an application, a short proof is given to the theorem that the…
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…
Given a renormalizable theory we construct the dilatation operator, in the sense of generator of RG flow of composite operators. The generator is found as a differential operator acting on the space of normal symbols of composite operators…
We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries…
A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…
The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta $ model are obtained in the frameworks of dynamical mapping method. The equivalence…
The relationship between associative composition algebras of dimensions 2 and 4 within the context of homogeneous spaces, with a particular focus on Hamiltonian quaternions, is explored. In the special case of Hamiltonian quaternions, the…
Motivated by the close connection of tensor models to the SYK model, we use representation theory to construct the complete set of gauge invariant observables for bosonic and fermionic tensor models. Correlation functions of the gauge…
Motivated by recent work of Au, C{\'e}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a…
We study the entanglement Hamiltonian for fermionic hopping models on rings and open chains and determine single-particle spectra, eigenfunctions and the form in real space. For the chain, we find a commuting operator as for the ring and…
This paper is devoted to studying $R$-diagonal and $\eta$-diagonal pairs of random variables. We generalize circular elements to the bi-free setting, defining bi-circular element pairs of random variables, which provide examples of…
Random graphs offer a useful mathematical representation of a variety of real world complex networks. Exponential random graphs, for example, are particularly suited towards generating random graphs constrained to have specified statistical…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
This article, which is substantially motivated by the previous joint work with J. McKay [8], establishes the analytic analogues of the relations we found free probability has with Witt vectors. Therefore, we first present a novel analytic…
We formulate the issue of minimality of self-adjoint operators on a Hilbert space as a semi-definite problem, linking the work by Overton in [1] to the characterization of minimal hermitian matrices. This motivates us to investigate the…
We study certain symplectic quotients of n-fold products of complex projective m-space by the unitary group acting diagonally. After studying nonemptiness and smoothness these quotients we construct the action-angle variables, defined on an…
In this paper we construct cumulants for stable random matrix models with single trace interactions of arbitrarily high even order. We obtain explicit and convergent expansions for it and we prove that it is an analytic function inside a…
Motivated by permutation statistics, we define for any complex reflection group W a family of bivariate generating functions. They are defined either in terms of Hilbert series for W-invariant polynomials when W acts diagonally on two sets…
Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…