相关论文: Free Bessel laws

We classify the centers of the quantized Weyl algebras that are PI and derive explicit formulas for the discriminants of these algebras over a general class of polynomial central subalgebras. Two different approaches to these formulas are…

The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. Recently Bernard and Jin have studied the fluctuations of the invariant measure for…

In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are…

The $\mathcal{A}$-tracial algebras are algebras endowed with multi-linear forms, compatible with the product, and indexed by partitions. Using the notion of $\mathcal{A}$-cumulants, we define and study the $\mathcal{A}$-freeness property…

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…

We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…

A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an uncertainity may be either an intrinsic property of a particle or can be viewed as an…

We address the question of identifying degrees of freedom for quantum systems. Typically, quasi-particle descriptions of correlated matter are based upon the canonical algebras of bosons or fermions. Here we highlight that a special class…

We present a simplified explanation of why free fractional convolution corresponds to the differentiation of polynomials, by finding how the finite free cumulants of a polynomial behave under differentiation. This approach allows us to…

Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we…

Poissonian pair correlations have sparked interest within the mathematical community, because of their number theoretic properties, and their connections to quantum physics and probability theory, particularly uniformly distributed random…

The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all…

We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…

A doubly infinite set of series expansion for $1/\pi$ are reported. They follow trivially from a formal expansion for the quotient of the values taken by the gamma function for two (complex) arguments differing by an integer plus one half,…

In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…

The coherent states are reviewed with particular application to the free particle system. The didactic advantages of the formalism is emphasized. Several interesting features, like the relation of the coherent states with the Galilei group…

This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of…

We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to $\varepsilon$-free independence, a mixture of classical and free independence studied by M{\l}otkowski and by Speicher and…

We consider the first hitting times of the Bessel processes. We give explicit expressions for the distribution functions and for the densities by means of the zeros of the Bessel functions. The results extend the classical ones and cover…