Related papers: Derivation of the Loop Hafnian Generating Function…
Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital $*$-subalgebra with core-like properties in its domain. On the other hand we prove that every…
The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…
We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. The deformation of…
The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay…
This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation…
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…
In this work, we study the computation of reduction coefficients for multi loop Feynman integrals using generating functions constructed within the Baikov representation. Compared with traditional Feynman rules, the Baikov formalism offers…
We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity…
If the prime numbers are pseudo-randomly distributed, then analogy with quantum systems suggests that counting primes might be modeled by a non-homogeneous Poisson process. Consequently, postulating underlying gamma statistics, more-or-less…
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational…
In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…
We present an overview of the role of generating functions in quantum mechanical contexts, mainly in the modern theory of polarization and in the study of quantum phase transitions. Generating functions enable the derivation of moments and…
We review existing methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has some advantages of simplicity and resource consumption…
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…
We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald…
We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include condensed matter systems with quenched disorder (e.g. spin glass) or cosmological systems in…
Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…
Gaussian boson sampling constitutes a prime candidate for an experimental demonstration of quantum advantage within reach with current technological capabilities. The original proposal employs photon-number-resolving detectors, however the…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlation functions for the eigen- and singular values at arbitrary…